A body is thrown upwards with a velocity of $20 m/s$. What is the time taken by the body to return to its initial position? (Take $g = 10 m/s^2$)

The displacement $x$ of a particle at the instant when its velocity v is given by $v = \sqrt {3x + 16} .$. Its acceleration and initial velocity are

A body is projected up with a speed ‘u' and the time taken by it is T to reach the maximum height H. Pick out the correct statement

An express train is moving with a velocity ${v_1}$. Its driver finds another train is moving on the same track in the same direction with velocity ${v_2}$. To escape collision, driver applies a retardation a on the train. The minimum time of escaping collision will be

A particle is moving with constant initial velocity 4 ${\rm{m}}{{\rm{s}}^{ - 1}}$ till t=1.5 s. Then it accelerates at 10 ${\rm{m}}{{\rm{s}}^{ - 2}}$ till t=3. The distance covered is (Take ${\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}$)

In a race for 100m dash, the first and the second runners have a gap of one metre at the mid way stage. Assuming the first runner goes steady, by what percentage should the second runner increases his speed just to win the race.

A ball is thrown vertically upwards. At the highest point of its trajectory, its acceleration is:

The displacement of a particle starting from rest (at t=0) is given by $s = 6{t^2} - {t^3}.$. The time in seconds at which the particle will attain zero velocity again, is

Two cars A and B at rest at same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with constant acceleration of $4m/{s^2}$, then B will catch A after how much time

A particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively.

The velocity of a body depends on time according to the equation $v = 20 + 0.1{t^2}.$ The body is undergoing