Motion in a Straight Line

A particle is moving in one dimension (along x axis) under the action of a variable force. Its initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as x = -3t3 + 18t2 + 16t, where x is in m and t is in s. The velocity of the particle when its acceleration becomes zero is m/s.

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h. Velocity of train B with respect to A and velocity of ground with respect to B are (in ms-1):

1. -50 and -30
2. -50 and 30
3. -30 and 50
4. 50 and -30

A particle initially at rest starts moving from reference point x=0 along x-axis, with velocity v that varies as v=4 x m/s. The acceleration of the particle is ms-2.

The relation between time 't' and distance 'x' is t= x2+ x, where and are constants. The relation between acceleration (a) and velocity (v) is :

1. a=-5 v5
2. a=-3 v2
3. a=-2 v3
4. a=-4 v4

A body starts falling freely from height H hits an inclined plane in its path at height h. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of Hh for which the body will take the maximum time to reach the ground is .

The displacement and the increase in the velocity of a moving particle in the time interval of t to (t+1) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in (t+2)th s is m.

A body starts moving from rest with constant acceleration covers displacement S1 in first (p-1) seconds and S2 in first p seconds. The displacement S1+S2 will be made in time :

1. (2p+1) s
2. (2p-1) s
3. (2p2-2p+1 )s
4. (2p2-2p+1 ) s

A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as x= (t3-6t2+20t+15 )m. The velocity of the body when its acceleration becomes zero is :

1. 6 m/s
2. 10 m/s
3. 8 m/s
4. 4 m/s

A bullet is fired into a fixed target loses one third of its velocity after travelling 4 cm. It penetrates further D 10-3 m before coming to rest. The value of D is :

1. 2
2. 5
3. 3
4. 4

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is m (use g=10 ms-2).