The velocity-time graph of a particle is given by $v = v_0(1-e^{-kt})$, where $v_0$ and $k$ are constants. The displacement of the particle at time $t$ is:

A stone thrown vertically upward files past a window one second after it was thrown upward and after three second on its way downward. The height of the window above the ground is (Take ${\rm{g}} = 10{\rm{m}}{{\rm{s}}^{ - 2}}$)

Velocity of a body on reaching the point from which it was projected upwards, is

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

A ball which is at rest is dropped from a height h metre. As it bounces off the floor its speed is 80% of what it was just before touching the ground. The ball then rise to nearly a height

A ball is dropped from top of a building. The ball take 0.5 s to fall past the 3 m length of window some distance from top of building with what speed does the ball pass the top of window?

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is

Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is $\left( {{\rm{g}} = 10{\rm{\;m}}{{\rm{s}}^{ - 2}}} \right)$

From the top of a tower, a stone is thrown up and reaches the ground in time ${t_1} = 9{\rm{s}}.$. A second stone is thrown down with the same speed and reaches the ground in time ${t_2} = 4$ s. A third stone is released from rest and reaches the ground in time ${t_3}$, which is equal to

Two particles held at different heights a and b above the ground are allowed to fall from rest. The ratio of their velocities on reaching the ground is

A ball of mass ${m_1}$ and another ball of mass ${m_2}$ are dropped from equal height. If time taken by the balls are ${t_1}$ and ${t_2}$ respectively, then