Two trains \(A\) and \(B\) of length \(400~\text m\) each are moving on two parallel tracks with a uniform speed of \(72~\text{km/h}\) in the same direction with \(A\) ahead of \(B.\) The driver of \(B\) decides to overtake \(A\) and accelerates by \(1~\text{m/s}^2.\) If after \(50~\text s,\) the guard of \(B\) just brushes past the driver of \(A,\) what was the original distance between them?
1. \(2000~\text m\)
2. \(2250~\text m\)
3. \(1200~\text m\)
4. \(1250~\text m\)
On a two-lane road, car \(A\) is travelling at a speed of \(36~\text{kmh}^{–1}.\) Two cars \(B\) and \(C\) approach car \(A\) in opposite directions with a speed of \(54~\text{kmh}^{–1}\) each. At a certain instant, when the distance \(AB\) is equal to \(AC,\) both being \(1~\text{km},B\) decides to overtake \(A\) before \(C\) does. What minimum acceleration of car \(B\) is required to avoid an accident?
1. \(1~\text{ms}^{-2}\)
2. \(5~\text{ms}^{-2}\)
3. \(2~\text{ms}^{-2}\)
4. \(3~\text{ms}^{-2}\)
A player throws a ball upwards with an initial speed of \(29.4 \text{ ms}^{- 1}.\) What is the direction of acceleration during the upward motion of the ball?
1. Vertically downwards
2. Vertically upwards
3. First upwards then downwards
4. None of the above
A particle in one-dimensional motion:
1. | with zero speed at an instant may have non-zero acceleration at that instant. |
2. | with zero speed may have non-zero velocity. |
3. | with constant speed, must have non-zero acceleration. |
4. | with a positive value of acceleration must be speeding up. |
A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?
1. | \(6\) km/h | 2. | \(5\) km/h |
3. | \(5.6\) km/h | 4. | \(6.6\) km/h |
The instantaneous speed is always:
1. | less than the magnitude of instantaneous velocity. |
2. | greater than the magnitude of instantaneous velocity. |
3. | equal to the magnitude of instantaneous velocity. |
4. | may be less or greater than the magnitude of instantaneous velocity. |
A police van moving on a highway with a speed of fires a bullet at a thief’s car speeding away in the same direction with a speed of . If the muzzle speed of the bullet is with what speed does the bullet hit the thief’s car?
The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) and \(3,\) respectively are:
1. | \(-,-,+\) | 2. | \(+,-,+\) |
3. | \(-,+,+\) | 4. | \(+,+,-\) |
The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?
1. | Interval 2 | 2. | Interval 1 |
3. | Interval 3 | 4. | Equal in all intervals |
A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to \(49~\text{ms}^{-1}.\) How much time does the ball take to return to his hands?
1. | \(5\) s | 2. | \(10\) s |
3. | \(15\) s | 4. | \(7\) s |