Q. No.When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity \({v_0}\) and the braking capacity, or deceleration, \(-a\) that is caused by the braking. Expression for stopping distance of a vehicle in terms of \({v_0}\) and \(a\) is:
1.
\(\dfrac{{v_o}^2}{2a}\)
2.
\(\dfrac{{v_o}}{2a}\)
3.
\(\dfrac{{v_o}^2}{a}\)
4.
\(\dfrac{2a}{{v_o}^2}\)
The position of an object moving along the \(x\text-\)axis is given by, \(x=a+bt^2\), where \(a=8.5 ~\text m,\) \(b=2.5~\text{m/s}^2,\) and \(t\) is measured in seconds. Its velocity at \(t=2.0~\text s\) will be:
1. \(13~\text{m/s}\)
2. \(17~\text{m/s}\)
3. \(10~\text{m/s}\)
4. \(0~\text{m/s}\)
A small block slides down on a smooth inclined plane starting from rest at time \(t=0.\) Let \(S_n\) be the distance traveled by the block in the interval \(t=n-1\) to \(t=n.\) Then the ratio \(\dfrac{S_n}{S_{n +1}}\) is:
| 1. | \(\dfrac{2n+1}{2n-1}\) | 2. | \(\dfrac{2n}{2n-1}\) |
| 3. | \(\dfrac{2n-1}{2n}\) | 4. | \(\dfrac{2n-1}{2n+1}\) |
A stone is released from an elevator going up with an acceleration \(a.\) The acceleration of the stone after the release is:
1. \(a\) upward
2. \((g-a)\) upward
3. \((g-a)\) downward
4. \(g\) downward
A person standing near the edge of the top of a building throws two balls \(A\) and \(B.\) The ball \(A\) is thrown vertically upward and \(B\) is thrown vertically downward with the same speed. The ball \(A\) hits the ground with a speed \(v_A\) and the ball \(B\) hits the ground with a speed \(v_B.\) We have:
| 1. | \(v_A>v_B\) |
| 2. | \(v_A<v_B\) |
| 3. | \(v_A=v_B\) |
| 4. | the relation between \(v_A\) and \(v_B\) depends on height of the building above the ground |
Mark the correct statements for a particle going on a straight line:
| (a) | if the velocity and acceleration have opposite sign, the object is slowing down. |
| (b) | if the position and velocity have opposite sign, the particle is moving towards the origin. |
| (c) | if the velocity is zero at an instant, the acceleration should also be zero at that instant. |
| (d) | if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval. |
Choose the correct option:
| 1. | (a), (b) and (c) | 2. | (a), (b) and (d) |
| 3. | (b), (c) and (d) | 4. | all of these |
Which of the following position-time \((x\text-t)\) graphs may be possible corresponding to given velocity-time \((v\text-t)\) graph?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A person sitting on the ground floor of a building notices through the window, of height \(1.5~\text{m}\), a ball dropped from the roof of the building crosses the window in \(0.1~\text{s}\). What is the velocity of the ball when it is at the topmost point of the window? \(\left(g = 10~\text{m/s}^2\right )\)
| 1. | \(15.5~\text{m/s}\) | 2. | \(14.5~\text{m/s}\) |
| 3. | \(4.5~\text{m/s}\) | 4. | \(20~\text{m/s}\) |
A ball is bouncing elastically with a speed of \(1~\text{m/s}\) between the walls of a railway compartment of size \(10~\text m\) in a direction perpendicular to the walls. The train is moving at a constant velocity of \(10~\text{m/s}\) parallel to the direction of motion of the ball. As seen from the ground:
| (a) | the direction of motion of the ball changes every \(10\) sec. |
| (b) | the speed of the ball changes every \(10\) sec. |
| (c) | the average speed of the ball over any \(20\) sec intervals is fixed. |
| (d) | the acceleration of the ball is the same as from the train. |
Choose the correct option:
| 1. | (a), (c), (d) | 2. | (a), (c) |
| 3. | (b), (c), (d) | 4. | (a), (b), (c) |
If in one-dimensional motion, instantaneous speed \(v\) satisfies \(0\leq v<v_0,\) then:
| 1. | the displacement in time \(T\) must always take non-negative values. |
| 2. | the displacement \(x\) in time \(T\) satisfies \(-{v_0T} \lt x \lt {v_0T}.\) |
| 3. | the acceleration is always a non-negative number. |
| 4. | the motion has no turning points. |
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