A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

• t³

• t²

• t

• t

A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flights in the two cases, then the product of the two time of flights is proportional to

• R²

• 1/R²

• 1/R

• 1/R

The relation between time t and distance x is t=ax² +bx where a and b are constants. The acceleration is

• −2abv²

• 2bv³

• −2av³

• 2av²

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then

• S=ft

• S= ft²/72

• S = 1/2 ft²

• S = 1/2 ft²

A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

• towards north-east
• towards north.

• zero

• zero

A parachutist after bailing outfalls 50 m without friction. When a parachute opens, it decelerates at 2 m/s². He reaches the ground with a speed of 3 m/s. At what height, did he bail out?

• 91 m

• 182 m

• 293 m

• 293 m

• π

• π/3

• π/2

• π/2

28.

A projectile can have the same range R for two angles of projection. If T₁ and T₂ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

• 1/R²

• 1/R

• R

• R

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

• The velocity vector is tangent to the circle.

• The acceleration vector is tangent to the circle.

• The acceleration vector points to the centre of the circle.

• The acceleration vector points to the centre of the circle.

A body of mass m accelerates uniformly from rest to v₁ in time t₁. The instantaneous power delivered to the body as a function of time t is