Motion in a Straight Line · Question 12

The position-time (x - t) graph for positive acceleration is

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sn be the distance travelled by the block in the interval t = n - 1 to t = n. Then the ratio SnSn+1 is :

1. 2n2n-1
2. 2n-12n
3. 2n-12n+1
4. 2n+12n-1

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s2)

1. 340 m
2. 320 m
3. 300 m
4. 360 m

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60 with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30 and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be :

1. 1 : 2
2. 2 : 1
3. 1 : 3
4. 1 : 2 3

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force q E, its velocity increases from 0 to 6 m s-1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

1. 2 m s-1, 4 m s-1
2. 1 m s-1, 3 m s-1
3. 1 m s-1, 3.5 m s-1
4. 1.5 m s-1, 3 m s-1

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On another day, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

1. t1t2t2-t1
2. t1t2t2+t1
3. t1-t2
4. t1+t22

If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is

1. 32A + 73B
2. A2 + B3
3. 32A + 4B
4. 3A + 7B

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t) = (at + bt2) and xQ(t) = (ft - t2). At what time do the cars have the same velocity ?

1. a-f1+b
2. a+f2(b-1)
3. a+f2(1+b)
4. f-a2(1+b)

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = x-2n, where and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

1. -2 2x-2n+1
2. -2n 2e-4n+1
3. -2n 2x-2n-1
4. -2n 2x-4n-1

A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is

1. h2 = 3h1 and h3 = 3h2
2. h1 = h2 = h3
3. h1 = 2h2 = 3h3
4. h1 = h23 = h35