The $x{\rm{ \;and \;}}y$ coordinates of the particle at any time are $x = 5t - 2{t^2}{\rm{ \;and\; }}y = 10t$ respectively, where $x{\rm{ \;and\; }}y$ are in meters and $t$ in seconds. The acceleration of the particle at $t = 2s$ is

Consider the acceleration, velocity and displacement of a tennis ball as it falls to the ground and bounces back. Directions of which of these changes in the process

A man of mass M stands at one end of a plank of length which is at rest on a frictionless horizontal surface. The man walks to the other end of the plank. If mass of the plank is M/3, the distance that the man moves relative to ground is

The displacement of two objects, $M$ and $N$, moving along a straight line are given by $x_M(t) = 2t + 4t^2$ and $x_N(t) = 8t - 2t^2$ respectively. At what time do they have the same velocity?

Particles $X$ and $Y$ move along a line. Their positions are described by $x_X(t) = 6t + 0.5t^2$ and $x_Y(t) = 4t - t^2$. Determine the time when both particles have the same instantaneous velocity.

Two bodies are moving along a straight line. The position of the first body is given by $x_1(t) = t + 2t^2$ and the position of the second body is given by $x_2(t) = 3t - t^2$. Find the time at which both bodies have the same speed.

A particle is moving in a straight line with velocity (v) = (t – 4) m/s. What is the average speed between t = 0 to t = 8 second?

A particle moves with a velocity given by $v = 6t - t^2$. What is the distance covered by the particle between $t = 0$s and $t = 2$s?

The acceleration of a particle is increasing linearly with time t as bt.The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time t will be

The velocity of a particle is given by $v = 2t + 3t^2$. What is the distance travelled by the particle between $t = 0$ s and $t = 1$ s?

A particle starts from rest and moves with uniform acceleration. After covering a distance $d$, its velocity becomes $v$. How much further will it travel before its velocity doubles to $2v$?