Motion in a Straight Line

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x = c0 (t2 - 2 ) + c(t - 2)2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. the acceleration of the particle is 2(c + c0)
2. the acceleration of the particle is 2c0
3. the acceleration of the particle is 2c
4. the initial velocity of the particle is 4c

A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next 32x distance. The average velocity in this motion is 507 m/s. If v1 is 5 m/s then v2 = m/s.

A sportsman runs around a circular track of radius r such that he traverses the path ABAB. The distance travelled and displacement, respectively, are [figure]

1. r, 3r
2. 2r, 3 r
3. 3 r, 2r
4. 3 r, r

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