Motion in a Straight Line

Two cars are travelling towards each other at speed of 20 m s-1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s-2. The distance between them when they come to rest is :

1. 25 m
2. 100 m
3. 50 m
4. 200 m

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h) :

1. 70
2. 40
3. 30
4. 80

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2. Time required to reach the ground, if it is dropped from the top of the tower, is :

1. t1 + t2
2. t1 t2
3. t1t2
4. t1 - t2

A particle moves in a straight line so that its displacement x at any time t is given by x2 = 1 + t2. Its acceleration at any time t is x-n where n = .

A body moves on a frictionless plane starting from rest. If Sn is distance moved between t = n - 1 and t = n and Sn-1 is distance moved between t = n - 2 and t = n - 1, then the ratio Sn-1Sn is (1 - 2x ) for n = 10. The value of x is .

A body travels 102.5 m in nth second and 115.0 m in (n+2)th second. The acceleration is :

1. 6.25 m/s2
2. 5 m/s2
3. 12.5 m/s2
4. 9 m/s2

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is: [figure]

1. 8 km
2. 4 km
3. 6 km
4. 8 km

A bus moving along a straight highway with speed of 72 km/h is brought to a halt within 4 s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is m.

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