The x-t plot shown in the figure below describes the motion of the particle, along x-axis, between two positions A and B. The particle passes through two intermediate points P₁ and P₂ as shown in the figure

• The instantaneous velocity is positive as P₁ and negative at P₂.

• The instantaneous velocity is negative at both P₁ and P₂

• The instantaneous velocity is negative at P₁ and positive at P₂

• The instantaneous velocity is positive at both P₁ and P₂

The graph which cannot possibly represent one-dimensional motion is

A man rides a bicycle with a speed of 17.32 ms^-1 East- West direction. If the rain falls vertically with a speed of 10 ms^-1, then the direction in which he must hold his umbrella is

• 30° with the vertical towards East

• 60° with the vertical towards West

• 30° with the vertical towards West

• 60° with the vertical towards East

From a balloon moving upwards with a velocity of12 ms^-1, a packet is released when it is at a height of 65 m from the ground. The time taken by it to reach the ground is (take, g = 10 ms^-2)

• 5 s

• 8 s

• 4 s

• 7 s

A bus is moving with a velocity of 10 ms^-1 on a straight road. A scootorist wishes to overtake the bus in one minute. If the bus is at a distance of 1.2 km ahead, then the velocity with which he has to chase the bus is

• 20 ms^-1

• 25 ms^-1

• 30 ms^-1

• 40 ms^-1

If the displacement of a body varies as the square of elapsed time, then its

• velocity is constant

• velocity varies non-uniformly

• acceleration is constant

• acceleration changes continuously

A ball dropped from a point A falls down vertically to C, through the mid-point B. The descending time from A to B and that from A to C are in the ratio

• 1 : 1

• 1 : 2

• 1 : 3

• $1 : \sqrt{2}$

The time required to stop a car of mass 800 kg, moving at a speed of 20ms^-1 over a distance of 25 m is

• 2 s

• 2.5 s

• 4 s

• 4.5 s

For a particle moving according to the equation $\mathrm{x} = \mathrm{a} \cos \mathrm{\pi } \mathrm{t},$ the displacement in 3 s is

• 0

• 0.5 a

• 1.5 a

• 2 a

The ratio of distance traversed in successive intervals of time when a body falls freely under gravity from certain height is

• 1 : 2 : 3

• 1 : 5 : 9

• 1 : 3 : 5

• $\sqrt{1} : \sqrt{2} : \sqrt{3}$