LINEAR MOTION
- a) The diagram below shows part of the motion of a tennis ball, which is projected vertically upwards from the ground and allowed to bounce on the ground. Use this information to answer questions that follow.
- i) Describe the motion of the ball relating it to different positions of the ball along the following AB, BC, CDE.
- ii) From the graph, calculate the acceleration due to gravity.
iii) How high does the ball rise initially?
- iv) Explain why E is not at the same level as A.
- Sketch a velocity- time graph showing the motion of a ball vertically upwards with an initial velocity of u.
- Calculate the acceleration shown by the tickers-tape that was made using a ticker timer vibrating at 50HZ.
- What is the difference between speed and velocity?
- An object is projected vertically upwards at a speed of 15m/s. How long will it take to return to the same level of projection?
- A block slides off a horizontal table 4 meters high with a velocity of 12-m/s. Find:
- a) The horizontal distance from the table at which the block hits the floor.
- b) The horizontal and vertical components of the velocity when it reaches the floor.
- A particle initially at A moves along an arc AB of a horizontal circle of radius 4m and centre O.A is south of O and angle AOB is 600. Determine the displacement AB.
- The figure represents dots made by a ticker-timer. The dots were made at a frequency of 50 dots per second. (Diagram not drawn to scale)
- a) What is time interval between two consecutive dots?
- b) The arrow on the tape indicates the dots made at time t = 0. Copy the diagram and
indicate in a similar way the dots made at t= 0.1s, 0.2s, 0.3s.
- c) Determine the average velocities of the tape over time intervals -0.02s to 0.02s, 0.08s to
0.12s, 0.18s to 0.22s and 0.28s to 0.32s
- d) Draw a suitable graph and from it determine the acceleration of the tape.
- A mass is projected horizontally from height of 5m above the ground with a velocity of 30m/s. Calculate:
- a) The time taken to reach the ground
- b) The horizontal distance travelled before hitting the ground
- c) The vertical velocity with which the mass hits the ground
- The data in the table below represents the motion over a period of 7 seconds
| Time s | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| D is m | 0 | 20 | 40 | 60 | 80 | 95 | 105 | 110 |
- a) Plot on graph paper a graph of displacement (y-axis) against time.
- b) Describe the motion of the vehicle for the first 4 seconds.
- c) Determine the velocities at 4.5s and 6.5 s. Hence or otherwise determine the average acceleration of the vehicle over this time interval.
- a) A body accelerates uniformly from initial velocity, U to the final velocity V, in time t, the distance traveled during this time interval is S. If the acceleration is shown by the letter a, show that;
- i) V= U + at ii) s= ut + ½ at2 iii) V2 =U2 + 2 as
- b) A body initially moving at 50m/s decelerates uniformly at 2m/s until it comes to rest. What distance does it cover from the time it started to decelerate?
- An object dropped from a height h attains a velocity of 6m/s just before hitting the ground, find the value of h.
- a) A stone is thrown vertically upwards from the edge of a platform eventually the stone lands without bouncing on the ground below the platform. Taking the upward velocity to be positive, sketch the velocity-time graph of the motion of the stone.
- b) A car can be brought to rest from a speed of 200m/s in a time of 2s.
- i) Calculate the average deceleration
- ii) If the driver reaction time is 0.2s, Determine the shortest stopping distance.
- The figure shows a speed-time graph for part of the journey of a motorcar.
Determine the distance the car travels in the first 40 seconds
- Draw axes and sketch a graph of velocity (v versus time (t) for uniformly accelerated motion given that when t = 0, v is greater than zero.
- a) The figure below shows the displacement time graph of the motion of a particle.
State the nature of the motion of the particle between:
- i) A and B
- ii) B and C
iii) C and D
- b) A ball is thrown horizontally from the top of a vertical tower and strikes the ground at a point 50m from the bottom of the tower. Given that the height of the tower is 45m, determine the;-
- i) Time taken by the ball to hit the ground
- ii) Initial horizontal velocity of the ball.
iii) Vertical velocity of the ball, just before striking the ground. (Take acceleration due to gravity g as 10ms-2)
- The graph bellows shows how the velocity varies with time for a body thrown vertically upwards.
Determine the total distance moved by the body.
- A bullet is fired horizontally from a platform 15m high. If the initial speed is 300ms-1, determine the maximum horizontal distance covered by the bullet.
- Fig 14 shows the velocity-time graph for a small metal sphere falling through a viscous fluid.
On the axes provided sketch the graph of momentum against time for the same mass
- The graph in figure 6 shows the velocity of a car in the first 8 seconds as it accelerates from rest along a straight line. Use the graph to answer question below
Determine the distance travelled 3.0 seconds after the start.
Determine the acceleration of the car at 4.0 seconds.
- A bomber flying horizontally at 100m/s releases a bomb from a height of 300m. Calculate:
- a) Time taken for the bomb to hit the ground.
- b) The horizontal distance travelled when hitting the ground.
- c) The magnitude and direction of the velocity when hitting the ground?
- An airplane is flying horizontally over a camp at 250m/s and drops a pack. How far from the camp will the pack land if the plane was flying 300m above the ground?
- An object is projected horizontally at a velocity of 40m/s from a cliff 20m high. Calculate:
- a) The time taken to hit the ground
- b) The distance from the foot of the cliff when the object hits the ground.
- A ball-bearing X is dropped vertically downwards, from the edge of a table and it takes 0.5s to hit the floor below. Another bearing Y leaves the edge of the table horizontally with a velocity of 5m/s. find:
- a) The time taken for bearing Y to reach the floor.
- b) The horizontal distance travelled by Y before hitting the floor.
- c) The height of the table-top above the floor level.
- A helicopter, which was ascending vertically at a steady velocity of 20m/s, released a parcel that took 20 second to reach the ground.
- i) State the direction in which the parcel moved immediately it was released.
- ii) Calculate the time taken by the parcel to reach the ground from the maximum height.
iii) Calculate the velocity of the parcel when it strikes the ground.
- iv) Calculate the maximum height above the ground the parcel reached.
- v) What was the height of the helicopter at the instant the parcel was dropped.
- A stone is thrown horizontally from a building that is 50 m high above a horizontal ground. The stone hits the ground at a point, which is 65m from the foot of the building. Calculate the initial of the stone.
- a) Distinguish between the terms ‘uniform velocity’ and ‘uniform acceleration’
- b) The figure below shows a section of a ticker tape. The dots were made at a frequency of 50 Hz. Determine the acceleration of the trolley pulling the tape
- c) The graph below shows a part of the motion of a basket ball which is projected vertically upwards from the ground and is allowed to bounce on the ground
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- i) Explain the motion of the ball relating it to its different positions along the following
I.AB II.BC III.CE
- ii) From the graph calculate the acceleration due to gravity
- One end of a metal rod is heated in a flame. After some time the other end becomes hot.
Explain this observation
- A bullet of mass 150g moving at an initial velocity of 80m/s strikes a suspended block of mass 2.5kg
- (a)The block swings from point A to B. Determine the vertical displacement between A and B
(b) What observations are you likely to observe on the block after collision
- The diagram below shows a velocity – time graph of a certain motion.
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From the graph, determine the average speed of the body.
- The figure 8 shows the motion of a train over a section of track which includes a sharp bend
- The section of the track with the sharp bend has a maximum speed restriction. The train decelerates approaching the bend so that at the start of the bend, it has just reached the maximum speed allowed. The train is driven around the bend at the maximum speed allowed and accelerates immediately on leaving the bend. Calculate the length of the bend
- The train has to slow down to go round the bend. Calculate the deceleration
- As the train is driven round the bend, there is extra force acting, called the centripetal force
- (a) The velocity-time graph in the figure below illustrates the motion of a ball which has been projected vertically upwards from the surface of the moon. The weight of the object on earth’s surface is 20N, when the acceleration due to gravity is 10ms-2.
- State why the velocity becomes negative after 3seconds.
- Determine the acceleration of free fall on the moon showing clearly your work
- Determine the total distance travelled by the ball in 5.0sec
- Find the weight of the ball on the moon
- If the ball was projected vertically upwards on the earth with the same velocity. What difference would you expect to observe in the velocity-time graph above. Illustrate with a sketch on the same axis
(b) The figure below represents part of a tape pulled through a ticker-timer of frequency 50Hz moving down an inclined plane.
If the trolley was allowed to move down the inclined plane for 4 seconds, calculate the distance it covers
- Figure 9 is a velocity- time graph describing the motion of a particle
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What does the shaded area represent?
- a) State Newton’s first law of motion
- b) A parcel is to be dropped from an aeroplane traveling horizontally at 120ms-1, at an altitude of 720m, to fall into a certain village.
Determine:
- i) The time taken for the parcel to reach the ground
- ii) How far ahead of the plane, the village should be when the parcel is released
- (a) Define uniform velocity
(b) The graph figure 10 below shows displacement –time graph of a in motion
fig 10
(i) Determine the instantaneous velocities at t = 1second and at t = 4 seconds
(ii) Use the results in (b)(i) above to determine the acceleration of the body
- A ball of mass 100g is kicked horizontally from the top of a cliff. If the ball takes 4 seconds to hit the ground, determine the height of the cliff
- A ball is kicked vertically upward from the ground with a velocity of 60m/s and reaches a maximum height (h), it then falls freely back to the ground and bounces upwards to a height of 5M
- Sketch a velocity-time graph to represent the motion of the ball from the time it is kicked vertically upwards until it bounces to a height of 5M
- Determine:
(i) The time taken by the ball to reach the maximum height (h)
(ii) The maximum height (h) reached by the ball
(iii) The velocity with which it bounces after striking the ground for the first time
- State any assumption made in your calculations in (b) above
- (a) State the three equations of linear motion.
(b) A car is travelling uniformly at 100km/hr when the driver observes a road block ahead. He takes 0.5 s before applying the brakes which brings the car to rest with a uniform deceleration of 4m/s2. Determine the distance travelled by the car from the time the driver observed the road block until the car comes to rest.
(c) A car moves at a constant speed of 20ms-1 for 50s and then accelerates uniformly to a speed of 25ms-1 over a period of 10s. This speed is maintained for 50 s before the car is brought to rest with uniform deceleration in 15s.
(d) Draw a graph of velocity (Y – axis) against time (graph paper to be availed)
(Calculate:
(i) The average speed for the whole journey.
(ii) The acceleration when the velocity changes from 20 ms-1 to 25ms-1 .
show that v2=2as +u2
- Sketch a velocity-time graph for a body moving with zero acceleration
- The figure below shows a velocity –time graph of a ball bouncing vertically upward from the ground. The velocity upward is taken positive.
Determine the maximum height when the ball rises.
- (a) On the axes provide below, sketch a graph of velocity V versus time (t) for uniformly accelerated motion given that when t = 0, V is greater than zero.
(b) A car is brought to Rest from a speed of 20 ms-1 in time of 2 seconds. Calculate the
deceleration.
- (a). State the law of linear momentum
(b). A marble of mass 50g moving on a horizontal surface at a velocity of V collides with another glass marble of mass 75g resting on same horizontal surface. After collision, the marble bounces back a long the path at a speed of 3.5m/s while the other marble moving with a speed of 3.0m/s .
Determine the speed V.
(c). The paper below was attached to a trolley and pulled through a ticker tape times of frequency 50Hz. Determine the acceleration of the trolley.
- A body accelerates uniformly from initial velocity of U m/s to a final velocity of V m/s in time t seconds. If acceleration during the motion is a m/s2 and the distance covered is S
- The data provided in table 1 shows the variation of displacement covered, by a train accelerating uniformly along a straight rail track, with time.
Table 1
| Time(s) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| Displacement(m) | 22.5 | 40.0 | 62.5 | 90.0 | 122.5 | 160.0 | 202.5 | 250.0 |
(a) On the grid provided, plot a graph of displacement (y – axis) against time (5mks)
(b) From the graph determine:
(i) The velocity at the 25th second (3mks)
(ii) The velocity at the 55th second (2mks)
(iii) The acceleration of the train (3mks)
- A tape is pulled steadily through a ticker timer of frequency 50Hz. The results are represented by the tape in the figure 4 below
Fig 4
Using the information above answer question 10 and 11
- Determine the average velocity of the body pulling the tape between
- i) AB
- ii) CD
- Determine the average acceleration of the body
- A body starts moving from rest and 10 seconds later it acquires a speed of 20m/s. It maintains a constant speed for 5 seconds. Finally the body undergoes uniform retardation to rest in 10 seconds
- a) Represent the motion graphically on the grid provided
- b) Determine the total distance covered
- c) Calculate the average speed of the body
- d) A stone is released from a height h, if the acceleration due to gravity is g, show that the velocity is v=2gh just before hitting the ground
- e) The diagram in the figure 5 below shows a smooth path AB in a vertical plane of a rolling bag of sugar placed at A.
Fig 5
It moves from A to B and flies off at B.
- If the mass of the bag is 100kg, calculate the change in its gravitation acceleration at potential energy between A and B
- Calculate the velocity of the bag at B if 80% of the potential energy becomes the kinetic energy.
- (a) For a body moving with a constant acceleration, a , show that:
(i) v = u + at where v and u are the final and initial velocities respectively while t is the time taken
(ii) S = ut + ½at2 where S is the distance covered
(iii) A car of mass 1200kg moving at 90km/h is brought to rest over a distance of 20m. Calculate the breaking force
(b) An object is projected vertically upwards with a velocity of 200m/s. Calculate:
(i) Its velocity after 5 seconds
(ii) The distance covered in the first 8 seconds
(iii) The maximum height reached
- a) The figure below shows a velocity time graph for a racing car.
Determine the total distance covered by a racing car?
- b) In an experiment, an object is dropped from a height h metres to a surface on the moon.The variation of vertical velocity (Ms-1) to time (s) from release is shown in the table 2, below.
| Velocity Ms-1 | 0.0 | 1.6 | 3.2 | 4.8 | 6.4 | 8.0 |
| Time (S) | 0 | 1 | 2 | 3 | 4 | 5 |
Table 2
(i) Plot a graph of vertical velocity against time.
(ii) From the graph, determine the height above the surface (h) from which the object is dropped if it only took 5 seconds to reach the ground..
(iii) From the graph, determine the acceleration due to gravity at the moon’s surface.
- The graph below shows how speed of a car varies as it travels between two towns on a horizontal road.
(a) (i) Determine the maximum speed of the car.
(ii) The acceleration of the car during the first two minutes of the journey.
(iii) The time during which the car is decelerating.
(iv) The total distance in metres between the two towns a long the road.
(v) The average speed in m/s .
(b) Describe the motion represented by lines
(i) PQ.
(ii) QR
(c ) Line OP is steeper than line QR. What does this show about the rates at which the car
speeds up and slows down ?
(d) A stone is allowed to fall freely from the top of a tower 60m high. At exactly the same time,
a second stone is thrown vertically upward with a velocity of 20m/s from the ground.
Determine the time taken by the two stones before they meet.
- Below is a velocity – time graph describing the motion of a particle
Determine the total displacement of the particle in the first 20 seconds
- Figure 7 shows a graph of velocity against time for a moving body
(a) (i) Describe the motion between O and B
(ii) Determine the acceleration between B and C
(b) A body moving initially at 50ms-1 decelerates uniformly at 2ms-2 until it comes to rest .
What distance does it cover from the time it started to decelerate?
(c) A car of mass1200kg is moving with a velocity of 25ms-1 round a flat bend of radius 150m. Determine:
(i) The minimum frictional force between the tyres and the road that will prevent the car from sliding off.
(ii) Coefficient of limiting static friction between the tyres and the surface
(d) The initial velocity of a body of mass 50kg is 10ms-1. A constant resultant force of 15N is then applied. How long will it take before the kinetic energy doubles?
- A stone was thrown vertically upwards with a velocity of 20m/s.
(i) State the acceleration of the stone at its maximum point
(ii) Calculate the time taken for the stone to fall back to the throwers hands
- A table tennis ball is dropped from a certain height a hard surface. On the axis below, sketch its velocity – time graph.
- a) Distinguish between speed and velocity.
- b) The figure below shows the motion of a ticker tape through a ticker – timer whose frequency is 100Hz.
Determine
- Velocity at AB and PQ.
II Constant acceleration of the tape.
- The figure 5 shows the displacement time graph for the motion of an object
Figure 5
Sketch on the axes provided the velocity time graph for the motion of the object (1mk)
- The diagram below (not drawn to scale) shows a velocity – time graph. Use it to answer the questions that follow.
- If the acceleration between points A and B is -1.25m/s2, determine the value of x
- Describe the motion of the body.
- Calculate the distance covered by the body during the whole journey.
- Figure shows the pattern formed on a tape in an experiment to determine the acceleration of a trolley. The figure is drawn to scale. The frequency of the ticker tape timer used was 50Hz.
Calculate
(i) The initial velocity of the trolley.
(ii) The final velocity of the trolley
(iii) The acceleration of the trolley.
(b) A gun is fired vertically upwards from the top of an open truck moving horizontally at a uniform velocity of 50ms-1. The bullet attains a maximum height of 45m. calculate the distance covered by the truck just before the bullet reaches the level from which it was fired.
- A car starts from rest; accelerates uniformly for 5 minutes to reach 30ms-1. It then continues at this speed for the next 20 minutes and then decelerates uniformly to come to stop in 6 minutes. On the axes provided below sketch the graph of velocity against time for the motion of the car.
Figure 5.
- Figure 8 shows dots which were made by a ticker timer-tape attached to a trolley.
Fig. 8
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If the frequency used was 50 Hz, determine
- a) The velocities between AB and BC
- b) The deceleration of the trolley.
- A body resting on a horizontal table is given an initial velocity U by pushing it so that it slides on the surface of the table for some time then it comes to a stop. The result of velocity and distance is tabulated below.
| Velocity U (m/s) | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 |
| Distance D (m) | 0.4 | 1.3 | 2.8 | 5 | 8 | 10 |
The equation relating U and D is given by U2 = 20wD where w is a constant for the surface. Plot an appropriate graph and use it to find w
- a) Define the term velocity.
- b) The following figure shows the velocity-time graph for the journey of a car in 100 minutes.
- Determine the acceleration of the car between A and B and between C and D.
- Determine the distance covered by the car during the journey.
- Determine the average velocity of the car.
- c) A ball rolls off o platform of height 1.8m at a horizontal speed of 15ms-1.How far off the edge of the platform does it land.
- An object is fired vertically upward from the ground level with a velocity of 50ms-1 and reaches a maximum height, h. It falls back to the ground and bounces to a height of 4m.
- Sketch a velocity time graph to represent the motion of the object from the time it is fired till it bounces to the height of 4m.
b.) Calculate the maximum height reached h.
- The tape in figure 9 below was obtained from an experiment using a ticker timer of frequency 50Hz. The tape was pulled by a trolley.
Figure 9
If the trolley that was pulling the tape was accelerating,
- i) Show on the diagram, the direction of acceleration of the trolley.
- ii) Calculate the acceleration of the trolley.
- b) A stone is allowed to fall freely from the top of a tower 60 metres high. At the same time, a second stone is thrown vertically upwards with a velocity of 20m/s from the ground. Find;
- i) The time taken by the two stones before they meet.
- ii) The height at which the two stones meet.
- The figure below represents part of a tape pulled through a ticker –timer by a trolley moving down an inclined plane. If the frequency of the ticker-timer is 50Hz, calculate the acceleration of the trolley.
(3mks)
- a) The table below show the values of the square of velocity (V2) and distance moved for uniformly accelerated lorry. Use the information in the table to answer the questions that follow.
| Distance, s (m) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
| Square velocity V2 ( m2/s2) | 4 | 29 | 54 | 79 | 104 | 129 | 154 |
- i) Plot a graph of V2 ( y-axis) against S.
- ii) From the graph, determine the acceleration of the car.
- b) (i) A body moving at 50ms-1 decelerates uniformly at 2ms-2 until it comes to rest. What distance does it cover from the time it starts to decelerate to the time it comes to rest?
(ii) How long does the body in b (i) above take to cover this distance?
- (a) The diagram shows a velocity-time graph for a vehicle.
The vehicle, moving at 4.0 m s-1 begins to accelerate at time = 0.
What is the vehicle’s acceleration at time = 3.0 s?
(b) A ball rolls off a platform of height 1.8m at a horizontal speed of 15ms-1. How far off the edge of the platform does it land.
(c) An arrow of mass 20g traveling horizontally strikes a block of wood of mass 1980g resting on a horizontal surface. The impact takes 0.2 seconds before the two move together with an initial velocity of 5m/s. Calculate:
(i) The velocity of the arrow before the impact.
(ii) The impulsive force.
(d ) A body initially moving at 50m/s decelerates uniformly at 20 m/s until it comes to rest. What distance does it cover from the time it started to decelerate?
- Figure 5 shows velocity-time gravity for a body.
Describe this motion.
- a) Figure13 shows the motion of stone moving vertically downwards as it goes with the tape from a ticker time.
If the ticker timer has a frequency of 100Hz, calculate the values of the acceleration due to gravity ‘g’
- a) Figure 7 shows a section of a ticker tape produced by a ticker-timer operating at a frequency of 50Hz.
Figure 7
Find the:
(i) Time for one tick interval.
(ii) Average velocity between A and B.
(iii) Average velocity between D and E
(iv) Average acceleration.
- b) A girl drops a stone from the top of a tower 45m tall. At the same time, a boy
standing at the base of the tower, projects another stone vertically upwards at
25ms-1 (g = 10 ms-2)
Determine the:
(i) time when the stones meet.
(ii) Point at which the stones meet
- The figure below shows the motion of a trolley on a ticker timer. The ticker has frequency of 50HZ
- (i) Calculate the initial velocity between A and B
(ii) Calculate the final velocity between C and D
(iii) Calculate the acceleration of the trolley during the motion
- A ball is dropped from the top of a vertical cliff 45m high. Given that the velocity just before striking the sandy beach is 30m/s and the ball penetrate the sand to a depth of 10cm. Determine its average retardation.
- c) Figure below shows a force distance graph for a car being towed on a level ground.
(i) Calculate the total work done
(ii) If the velocity just before reaching point C is 0.6m/s. Calculate the power
developed by the engine at this point
- Figure 7 shows a displacement – time graph
Describe the motion of the body between points.
(i) OA
(ii) AB
- A ball is thrown horizontally from the top of a vertical tower and strike the ground at a point 50m from the bottom of the tower. Given that the height of the tower is 45m, determine the
(i) Time taken by the ball to hit the ground.
(ii) The initial horizontal velocity of the ball.
(iii) Vertical velocity of the ball just before striking the ground.
