The two ends of a train moving with constant acceleration pass a certain point with velocities u and 3u. The velocity with which the middle point of the train passes the same point is

(1) 2u

(2) $\frac{3}{2}u$

(3) $\sqrt{5}u$

(4) $\sqrt{10}u$

A train starts from rest from a station with acceleration 0.2 m/s² on a straight track and then comes to rest after attaining maximum speed on another station due to retardation 0.4 m/s². If total time spent is half an hour, then the distance between two stations is- [Neglect length of train]

(1) 216 km

(2) 512 km

(3) 728 km

(4) 1296 km

A body is projected vertically in the upward direction from the surface of the earth. If the upward direction is taken as positive, then the acceleration of the body during its upward and downward journey is:

1. Positive, negative

2. Negative, negative

3. Positive, positive

4. Negative, positive

A particle starts moving from rest state along a straight line under the action of a constant force and travel distance x in first 5 seconds. The distance travelled by it in the next five seconds will be

(1) x

(2) 2x

(3) 3x

(4) 4x

A body is projected vertically upward with a speed 40 m/s. The distance travelled by the body in the last second of the upward journey is [take g = 9.8 m/s² and neglect effect of air resistance]

(1) 4.9 m

(2) 9.8 m

(3) 12.4 m

(4) 19.6 m

A body is projected vertically upward with a speed 10 m/s and another at the same time with the same speed in the downward direction from the top of a tower. The magnitude of acceleration of first body with respect to second is {take g = 10 m/s²}

(1) Zero

(2) 10 m/s²

(3) 5 m/s²

(4) 20 m/s²

A car travelling at a speed of 30 km/h is brought to rest at a distance of 8 m by applying brakes. If the same car is moving at a speed of 60 km/h, then it can be brought to rest with the same brakes in:

1. 64 m

2. 32 m

3. 16 m

4. 4 m

A particle is thrown with any velocity vertically upward, the distance travelled by the particle in the first second of its descent is:

(1) g

(2) $\frac{g}{2}$

(3) $\frac{g}{4}$

(4) Cannot be calculated

A body is thrown vertically upwards and takes 5 seconds to reach maximum height. The distance traveled by the body will be the same in

(1) 1^st and 10^th second

(2) 2^nd and 8^th second

(3) 4^th and 6^th second

(4) Both (2) & (3)

A ball is dropped from a bridge of 122.5 metre above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. Initial velocity of the second ball so that both hit the water at the same time is

(1) 49 m/s

(2) 55.5 m/s

(3) 26.1 m/s

(4) 9.8 m/s