Motion in a Straight Line

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is .

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4 s? [figure]

1. 11 m
2. 30 m
3. 13 m
4. 10 m

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is km . [figure]

1. 12
2. 6
3. 3
4. 9

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is :

1. 9.2 m/s
2. 8.8 m/s
3. 10 m/s
4. 8 m/s

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