Physics 30S Kinematics Graphs Review
Short Answer
1. Find the velocity in each section of the following position-time graph.
2. Find the average velocities for the intervals AB and BC.
3. Using the graph, determine the average velocity for each of the following sections.
(a) t = 0 s to t = 2 s
(b) t = 6 s to t = 12 s
(c) t = 6 s to t = 15.5 s
4. Using the graph, determine each of the following.
(a) the average velocity for the first 2.5 s
(b) the average velocity for the interval 2.5 to 7.5 s
(c) the instantaneous velocity at the points A, B, and C
(d) the times at which the instantaneous velocity is approximately zero
5. The following graph is that of an object moving in a straight line. East is considered as the positive direction.
(a) Determine the position of the object at t = 7.0 s.
(b) The graph shows five distinct sections. Briefly, and in general terms, describe the motion of the object in
each of these sections.
(c) Considering the whole journey, calculate the average velocity.
(d) Find the instantaneous velocity at t = 13 s.
(e) Using an appropriate scale, draw a velocity-time graph from the position-time graph.
6. This graph describes the motion of an object moving in a straight line. At the beginning it is going east. From
the graph determine each of the following.
(a) the object’s displacement in the first 3.0 s
(b) the object’s displacement between t = 3.0 s and t = 5.0 s
(c) the total displacement of the object in 14 s
(d) the average velocity of the object from t = 0 to t = 8.0
(e) the d-t graph; use it to check your answers to parts (a) to (d)
7. From this graph determine the acceleration for each interval, using the slopes.
8. From the v-t graph below, draw the corresponding d-t graph and a-t graph. (Assume that d1 = 0.)
9. (a) Which sections of this graph represent
(i) uniform velocity
(ii) the object at rest
(iii) acceleration
(b) What is the average velocity in the intervals
(i) t = 0 s to t = 5.0 s
(ii) t = 15 s to t = 20 s
(c) What is the instantaneous velocity at
(i) t = 3.0 s
(ii) t = 24 s
(iii) t = 8.0 s
10. The v-t graph on the next page represents the motion of a car. Assume that north is positive.
(a) In which interval(s) is the velocity uniform?
(b) In which interval(s) is the acceleration uniform?
(c) How far has the car travelled after (i) 11 s and (ii) 25 s?
(d) How far did the car travel in the 13th second?
(e) What is the acceleration (i) in the first 5.0 s and (ii) from t = 11 s to t = 14 s?
(f) What is the instantaneous acceleration at (i) t = 12.5 s and (ii) t = 22 s?
Kinematics Graphs Review
Answer Section
SHORT ANSWER
1. ANS:
KEY: FOP 2.3, p.49
2. ANS:
MSC: P
Interval AB
Interval BC
KEY: FOP 2.3, p.51
3. ANS:
(a)
(b)
MSC: SP
(c)
KEY: FOP 2.4, p.52
4. ANS:
MSC: P
(a)
(b)
(c)
(d) The instantaneous velocity is approximately zero when the slope of the d-t graph is approximately zero. This
occurs at t = 8.2 s, 12.5 s, 14.5 s.
KEY: FOP 2.5, p.54
MSC: P
5. ANS:
(a) Position after 7.0 s is –10 m or 10 m [W].
(b)
(i) t = 0 to t = 4.0 s
Uniform velocity of 2.5 m/s [W].
(ii) t = 0 to t = 7.0 s – stopped.
(iii) t = 7.0 s to t = 9.0 s
Uniform velocity of 7.5 m/s [E].
(iv) t = 7.0 s to t = 11.0 s
Uniform velocity of approximately 1.3 m/s [W].
(v) t = 11.0 s to t = 14.0 s
Uniform acceleration in the easterly direction.
(c)
(d)
(e)
KEY: FOP 2.6, p.56
6. ANS:
MSC: P
(a)
(b) Displacement
0m
(c)
(d)
(e)
KEY: FOP 2.7, p.59
7. ANS:
MSC: P
KEY: FOP 2.8, p.62
8. ANS:
MSC: P
KEY: FOP 2.12, p.69
MSC:
9. ANS:
(a) Uniform velocity – A, B, D, E
At rest – B
Acceleration – C
P
(b) (i)
(ii)
(c) (i) Since the graph is a straight line for this interval, the velocity is uniform and will have the same value as
(i) in part (b), that is, 1.4 m/s.
(ii)
(iii)
KEY: FOP 2.15, p.80
10. ANS:
(a) B, D
(b) A, C
(c) (i)
(ii)
MSC:
P
(d) From t = 12 s to t = 13 s
(e) (i)
(ii)
(f) (i)
(ii)
KEY: FOP 2.15, p.80
MSC:
P