Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of `72 km h^-1` in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by `1 m//s^-2`. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

Two straight wires A and B of lengths 10 m cach carrying currents of 4.0 A and 6.0 A in opposite directions lic parallel to each other at a distance of 2 cm. Estimate the force on a 10 cm section of the wire B near its centre.

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s~1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of 10 m s^1 (b) downwards with a uniform acceleration of 5 m s^2, upwards with a uniform acceleration of 5 m s-^1z. What would be the readings on the scale in each case? What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km h~1 in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed - (assumed constant) do the buses ply on the road?

A trolley of mass 200 kg moves with a uniform speed of 36 km/ h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Onna two-lane road, car A is travelling with a speed of 36 km h_1. Two care B and C approach car A in opposite directions with a speed of 54'km h_1 each. vAt 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?

Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m/s and 1 m/s, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Determine the velocity of the second object.

A police van moving on a highway with a speed of 30 km h_ 1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h^-1 . If the muzzle speed of the bullet is 150 m s^1 with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

A driver of a car travelling at 52 km h^-1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h^-1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelle farther after the brakes were applied?

Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train,(b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,just after it is dropped from the window of a train accelerating with 1 ms^2,just after it is dropped from the window of a train accelerating with 1M/S2