Q.8
The minimum time T required for a car to safely overtake a lorry is illustrated in the given diagram. It is measured from the time the front of the car is level with the rear of the lorry, until the rear of the passing car is a full car-length ahead of the front of the lorry.
The lorry may be taken to be 17.0 m long and the car 3.5 m long. The given graph shows how the speeds v of the car and the lorry vary with time t.
What is the value of T?
A 0.86 s B 1.2 s
C 2.6 s D 3.0 s
Answer: D
Just after car safely overtakes, its displacement relative to lorry,
d = lorry length + 2 x car length
d = (17.0) + 2 x (3.5) = 24.0 m
From v-t graph,
d ≡ (area under graph for car) – (area under graph for lorry)
i.e. (24.0) = ½ (10+26)T – 10T
24.0 = 8T
So, T = 3.0 s
Q.9
A car is moving along a straight line. The given graph shows how the velocity v of the car varies with time t. During which of the given time intervals does the car’s acceleration have its greatest numerical value?
Answer:
Acceleration = rate of change of velocity
Acelleration ≡ rate of change of the slope of displacement – time graph
Among the gives options, the slope of the graph is changing in interval A only.
Q.10
At time t = 0, a steel ball is thrown upwards from the top of a cliff. After rising to its maximum altitude, the ball falls past the cliff-top and into the sea. The graph shows the variation with time t of velocity v of the ball. The magnitudes of the areas of the two trangles are S and R, as shown.
Which expression given the height of the cliff-top above the sea?
A R B S C R + S D R – S
Answer: D
S ≡ distance travelled by stone from top of cliff to maximum height
R ≡ distance travelled by stone from maximum height to the sea
Height of the cliff-top above the sea = R – S
Q.11
A ball is held above rigid horizontal surface and released so that it falls on the surface and rebounds several times. The given graph describes the motion of the ball after being released.
What is represented by the quantity y?
Answer:
For a bouncing ball, only the displacement (downward positive) would ‘bounce off’ a fixed value.
Q.12
A ball is released from rest above a horizontal surface and is allowed to bounce. The given graph shows how its velocity v varies with time t. (The downward direction is taken as positive.)
At which of the given times on the graph does the ball reach its maximum height after bouncing?
Answer:
Height is maximum when ball stop rising, i.e. when its velocity becomes zero from an upward velocity.
Since downward is positive, height is maximum at D, when its velocity become zero from negative (upward).
Q.13
The graph shows the variation with time t of the displacement s of an object moving in a straight line.
Which of the following graphs best represents the corresponding variation of velocity v with time t?
Answer:
v ≡ gradient of s-t graph
v > 0 around t = 0, v = 0 around mid point,
Only C fits.
Q.14
A trolley is projected up an inclined runway at time t = 0. The variation its velocity with time t is as shown in the given graph.
What is the maximum distance up the runway reached by the trolley?
A 0.80 m B 1.0 m
C 2.0 m D 4.0 m
Answer:
Distance is maximum when v = 0.
Maximum distance up the slope
= area under v-t graph (above v = 0)
= ½ x 0.80 x 2.5 = 1.0 m
Q.15
The given graph shows the variation with time of the acceleration of a car travelling along a straight road. At whit of the given points on the graph does the velocity of the car has greatest value?
Answer: C
Velocity of car is maximum when it stop increasing, i.e. when acceleration becomes zero from a positive value.
Velocity is maximum at C.
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