Q.1
For a particle accelerating along a straight line, what is the definition of its velocity?
A Velocity is displacement divided by time.
B Velocity is distance divided by time.
C velocity is the rate of change of displacement
D Velocity is the rate of change of distance.
Answer: C
Velocity is the rate of change of displacement (with respect to time) (or change in displacement per unit time)
Q.2
Which of the following gives the acceleration of a body?
A the area under its displacement-time graph
B the area under its velocity-time graph
C the area gradient of its displacement-time graph
D the area gradients of its displacement-time graph
Answer: D
Acceleration = rate of change of velocity ≡ gradient of velocity-time graph
Q.3
After accelerating down a hill, a cyclist moves at constant speed and then decelerates as he climbs up another hill. Which graph show the variation of distance s traveled by the cyclist with time t?
Answer: D
First part: acceleration, i.e. increasing speed
first part of s-t graph is concave upwards
Mid-part: constant speed
mid part is a straight line
Final part: deceleration, i.e. decreasing speed
final part is concave downwards
Only D fits
Q.4
The given graph shows the variation with time of the velocity of a moving body.
Which graph best represents the corresponding variation of displacement with time?
Answer:
1st interval: constant acceleration,
displacement ∝ t2, concave upwards
2nd interval: constant velocity
displacement ∝ t, straight line
3rd interval: constant deceleration,
displacement ∝ -t2, concave downwards
Only C fits.
Q.5
The average speeds of a car, accelerating uniformly through three gear changes, are as shown.
| 20 m s-1 for 2.0 s 40 m s-1 for 2.0 s 60 m s-1 for 6.0 s |
What is the overall average speed of the car?
A 12 m s-1 B 13.3 m s-1
C 40 m s-1 D 48 m s-1
Answer:
Overall average speed = overall distance/overall duration
= ∑(average speed x duration)/∑duration
= {(20 x 2.0) + (40 x 2.0) + (60 x 6.0)}/(2.0 + 2.0 + 6.0)
= 48 m s-1
Q.6
A car is traveling with uniformly increasing speed along a straight road.
Which graph best represents the motion of the car?
Answer: A
A uniformly increasing speed
a uniform acceleration.
Q.7
A steel ball is released from rest a distance above a rigid horizontal surface and bounces several times. The diagram shows how its velocity varies with time.
Which statement correctly explains why the areas X and Y are equal?
A The ball’s acceleration is the same during its upward and downward motion
B The speed at which the ball leaves the surface after an impact is equal to the speed at which it returns to the surface for the next impact.
C For one impact, the speed at which the ball hits the surface equals the speed at which it leaves the surface.
D The ball rises and falls through the same distance between impacts.
Answer: D
Area under the v-t graph (downward positive) is the distance travelled.
The ball must rise and fall through the same distance between impacts.
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