A block is kept on a frictionless inclined surface with angle of inclination α. The incline is given an acceleration a to keep the block stationary. Then a is equal to

• g/tanα

• g cosecα

• g

• g

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function time is given by

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

• x²

• e^x

• x

• x

4.

A ball is thrown from a point with a speed ν₀ at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed ν₀/2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

• yes, 60°

• yes, 30°

• no

• no

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

The following figure gives the movement of an object. Select the correct statement from the given choices.

• The total distance travelled by the object is 975 m

• The maximum acceleration of the object is 2m/s²

• The maximum deceleration happend between 25th and 85th seconds

• The object was at rest between 10th and 15th seconds

Two object P and Q, travelling in the same direction starts from rest. While the object P starts at time t = 0 and object Q starts later at t = 30 min. The object P has an acceleration of 40 km/h². To catch P at a distance of 20 km, the acceleration of Q should be

• 40 km/h²

• 80 km/h²

• 160 km/h²

• 120 km/h²

A train of length L move with a constant speed V_t. A person at the back of the train fires a bullet at time t = 0 towards a target which is at a distance of D (at time t = 0) from the front of the train (on the same direction of motion). Another person at the front of the train fires another bullet at time t = T towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets V_b are same, the length of the train is

• T × (V_b × 2V_t)

• T × (V_b + V_t)

• $\frac{2{\mathrm{V}}_{\mathrm{b}}\mathrm{D}}{{\mathrm{V}}_{\mathrm{b}} + {\mathrm{V}}_{\mathrm{t}}} + \mathrm{T} \left({\mathrm{V}}_{\mathrm{b}} - {\mathrm{V}}_{\mathrm{t}}\right)$

• T × (V_b − 2V_t)

A person from a truck, moving with a constant speed of 60 km/h, throws a ball upwards with a speed of 60 km/h. Neglecting the effect of Earth and choose the correct answer from the given choice.

• The person cannot catch the ball when it comes down since the truck is moving

• The person can catch the ball when it comes down, if the truck is stopped immediately after throwing the ball

• The person can catch the ball when it comes down, if the truck continues to move with a constant speed of 60 km/h

• The person can catch the ball when it comes down, if the truck moves with speed more than 60 km/h

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