A point p moves in counter -clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out the length s = t3 + 5, where s is metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2 s is nearly

• 13 ms^-2

• 12 ms^-2

• 7.2 ms^-2

• 7.2 ms^-2

A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is 1/8 mv₀²,the value of k will be

• 10^-4 kg m^-1

• 10^–1 kg m^–1 s^–1

• 10^-3 kg m^-1

• 10^-3 kg m^-1

A time-dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be

• 9J

• 18 J

• 4.5 J

• 4.5 J

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

A particle has an initial velocity of  and an acceleration of It speed after 10 s

• 10 units

• 

• 7 units

• 7 units

16.

A motorcycle starts from rest and accelerates along a straight path at 2 m/s². At the straight point of the motorcycle, there is a stationary electric siren. How far has the motorcycle gone when the driver hears the frequency of the siren at 94% of its value when the motorcycle was at rest?

• 49 m

• 98 m

• 147 m

• 147 m

Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate.Assume that the duration of collision is negligible and the collision with the plate is totally elastic.Then the velocity as a function of time and the height as a function of time will be

A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-directionn with a constant speed. The position of the first body is given by x1(t) after time ‘t’ and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x₁ – x₂)as a function of time ‘t’?

The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

• v₀ + 2g + 3f

• v₀ + g/2 + f/3

• v₀ + g + f

• v₀ + g + f

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000. N/m. The spring compresses by

• 5.5 cmYes

• 2.5 cm

• 11 cm

• 11 cm