Two trains A and B of length \(400\) m each are moving on two parallel tracks with a uniform speed of \(72\) km/h in the same direction with A ahead of B. The driver of B decides to overtake A and accelerates by \(1\) m/s2. If after \(50\) s, the guard of B just brushes past the driver of A, what was the original distance between them?
1. \(2000\) m
2. \(2250\) m
3. \(1200\) m
4. \(1250\) m
On a two-lane road, car A is travelling at a speed of \(36\) kmh–1. Two cars B and C approach car A in opposite directions with a speed of \(54\) kmh–1 each. At a certain instant, when the distance AB is equal to AC, both being \(1\) km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?
1. \(1\) ms–2
2. \(5\) ms–2
3. \(2\) ms–2
4. \(3\) ms–2
A player throws a ball upwards with an initial speed of . 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 \(1,\) \(2\) & \(3,\) 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