Graphs - straight line motion 1.

How does the slope (or gradient) of a velocity-time graph for a moving object depend on the size of the object’s acceleration?

2.

Sketch the shape of a velocity-time graph for an object moving with a decreasing acceleration, starting from rest.

3.

Sketch the shape of a velocity-time graph for the motion of an object which starts at rest and has an increasing acceleration.

4.

Which quantities are calculated by the areas under: (a) a speed-time graph

(b) a velocity-time graph?

5.

Sketch the velocity-time graph for the first three bounces of a ball dropped vertically from rest, assuming that some mechanical energy is lost during each bounce.

6.

Sketch the likely shape of the speed-time graph for the motion of a stone released from rest from the surface of a deep loch.

7.

Sketch a speed-time graph for an object which moves with decreasing deceleration from a starting speed ‘u’ to rest in ‘t’ seconds.

8.

Sketch a possible speed-time graph for a sky diver from the instant of jumping out of a stationary balloon till just before the parachute is opened when he is travelling with a terminal velocity of 60 m/s.

9.

Describe the shape of graph which would be obtained if, for a moving object of a certain mass, its kinetic energy at different velocities was plotted against the square of its velocity.

10.

Which quantities are found from the areas under the lines of: (a)

a force-time graph

(b)

an acceleration-time graph? a

F

t

t 11.

Which quantities are found from the gradients of: (a)

12.

velocity-time graphs

(b)

distance-time graphs?

The areas under which graphs would calculate, for an object: (a)

change of momentum

(b)

distance

(c)

change of velocity?

The gradient of a velocity-time graph at one point is found to be 2.5. If the velocity is measured in ‘metres per second’ and the time in ‘seconds’, state the value of the acceleration at that point?

14.

Describe the motion of the object for which the distance-time graph has been constructed.

distance

13.

15.

Describe the motion of the object for which the distance-time graph has been constructed.

distance

time

16.

Describe the motion of the object for which the distance-time graph has been constructed.

distance

time

17.

Describe the motion of the object for which the distance-time graph has been constructed.

distance

time

18.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

time

time

For the motion described by the velocity-time graph in Q18, sketch a possible distance-time graph.

20.

In Q18, what is the gradient of the velocity-time graph?

21.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

19.

0 22.

time

For the motion described by the velocity-time graph in Q21, sketch:

23.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

(a) a possible distance-time graph (b) a possible acceleration-time graph.

0 For the motion described by the velocity-time graph in Q23, sketch a possible acceleration-time graph.

25.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

24.

time

0 For the motion described by the velocity-time graph in Q25, sketch a possible acceleration-time graph.

27.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

26.

time

time

For the motion described by the velocity-time graph in Q27, sketch a possible acceleration-time graph.

29.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

28.

0 For the motion described by the velocity-time graph in Q29, sketch a possible acceleration-time graph.

31.

Describe the motion of the object for which the velocity-time graph has been constructed.

velocity

30.

time

0 For the motion described by the velocity-time graph in Q31, sketch a possible acceleration-time graph.

33.

Describe the motion of the object for which the acceleration-time graph has been constructed.

acceleration

32.

time

time 34.

For the motion described by the acceleration-time graph in Q33, sketch: (a) a possible velocity-time graph and (b) a possible distance-time graph. For the velocity-time graphs, which show the motion of two vehicles, A and B, state which vehicle: (a)

has the greater acceleration,

(b)

reaches the higher speed and

(c)

covers more distance.

A

velocity

35.

0

B

time

36.

In Q35, is the acceleration of each vehicle uniform or non-uniform?

37.

Sketch a possible velocity-time graph for an object moving with a uniform negative acceleration.

38.

Describe the motion of the vehicle as shown in the speed-time graph below.

speed in m/s

20

10

0

0

5

10

15

20 time in s

39.

For the motion described by the speed-time graph in Q38, calculate (a) the distance moved in the first 5 s, (b) the total distance moved, (c) the average speed of the vehicle and (d) the acceleration over the first 5 s. Describe the motion of the vehicle as shown in the speed-time graph below.

speed in m/s

40.

40

20

0 41.

0

5

10

15

20 time in s

For the motion described by the speed-time graph in Q40, calculate (a) the distance moved in the first 5 s, (b) the distance moved in the first 10 s, (c) the total distance moved, (d) the average speed of the vehicle and (e) the deceleration over the last 5 s.

42.

Describe the motion of the vehicle as shown in the speed-time graph below.

speed in m/s

20

10

0

43.

0

5

10

15

20 time in s

For the motion described by the speed-time graph in Q42, calculate (a) the distance moved in the first 10 s, (b) the distance moved in the first 15 s, (c) the total distance moved, (d) the average speed of the vehicle (e) the smaller acceleration and (f) the larger acceleration.

44.

Which two criteria must be met for a line graph to indicate direct proportionality between two quantities?

45.

Given a table of data with pairs of values for the kinetic energy and speed of a moving object, which graph would be drawn to show the mathematical relationship between the two quantities, by a straight line through the origin?

46.

Given data consisting of pairs of velocity-time measurements for an object accelerating uniformly from rest, what graph could be constructed using the measurements which would be a straight line through the origin?

47.

Given data consisting of pairs of distance-time measurements for an object accelerating uniformly from rest, what graph could be constructed using the measurements which would be a straight line through the origin?

48.

Draw a speed-time graph for the motion of a car described thus: “the car starts from rest and accelerates uniformly to a top speed of 15 m/sin 5 s. It remains at this speed for 10 s before decelerating uniformly to rest in 10 s”. Calculate the acceleration during the first 5 s and the distance travelled over the whole journey.

49.

Draw a speed-time graph for the motion of a car described thus: “the car starts from rest and accelerates uniformly to a speed of 10 m/s in 4 s. It stays at this speed for 6 seconds and then accelerates uniformly over 5 s to a top speed of 20 m/s. It travels at this speed for a further 5 s before decelerating uniformly to rest. The total motion lasts for 30 s”. Calculate the value of the larger acceleration, the total distance moved and the average speed of the car. For the velocity- time graph, calculate: (a)

the acceleration

(b)

the distance moved

20 velocity in m/s

50.

0

10 time in s

0 For the velocity- time graph, calculate: (a)

the acceleration

(b)

the distance moved

25 velocity in m/s

51.

0 0

For the velocity- time graph, calculate: (a)

the acceleration

(b)

the distance moved

30 velocity in m/s

52.

10 time in s

0 0

10 time in s

For the velocity- time graph, calculate: (a)

the acceleration

(b)

the distance moved

20

velocity in m/s

53.

10

0 0

For the velocity- time graph, calculate: (a)

the acceleration

(b)

the distance moved

velocity in m/s

54.

4 time in s

20

10 4

55.

For the acceleration-time graph of a moving object, calculate: (a)

the change of velocity

(b)

the final velocity if the acceleration started when the object was moving at 10 m/s

acceleration in m/s2

0 0

2

0 0

56.

8 time in s

For the motion described by the acceleration-time graph in Q55, construct the corresponding velocity-time graph. From the velocity-time graph, calculate the total distance moved.

6 time in s

For the acceleration-time graph of a moving object, calculate: (a)

the change of velocity

(b)

the final velocity if the acceleration started when the object was at rest.

acceleration in m/s2

57.

3

0

5

2

time in s

-2

For the motion described by the acceleration-time graph in Q57, construct the corresponding velocity-time graph for the whole motion. From the velocity-time graph, calculate the total distance moved.

59.

For the acceleration-time graph of a moving object, calculate: (a)

the change of velocity

(b)

the final velocity if the acceleration started when the object was at rest.

acceleration in m/s2

58.

6

3

0 0

2

4

6 time in s

For the motion described by the acceleration-time graph in Q59, construct the corresponding velocity-time graph for the whole motion. From the velocity-time graph, calculate the total distance moved.

61.

For the acceleration-time graph of a moving object, calculate: (a)

the change of velocity

(b)

the final velocity if the acceleration started when the object was moving at 20 m/s.

acceleration in m/s2

60.

8

4

0 0

62.

5

10 15 time in s

For the motion described by the acceleration-time graph in Q61, construct the corresponding velocity-time graph for the whole motion. From the velocity-time graph, calculate the total distance moved