A particle moving with uniform acceleration along a straight line covers distances $S_1$ and $S_2$ in successive time intervals $t_1$ and $t_2$. Which equation correctly relates these quantities?

One car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is

The relation between time t and distance x is $t = a{x^2} + bx,$ where a and b are constants. The acceleration is

If the velocity of a particle is $\upsilon \,{\rm{ = }}\,{\rm{At}}\,{\rm{ + }}\,{\rm{B}}{{\rm{t}}^2}$, where A and B are constants, then the distance travelled by it between 1s and 2s is:

A bus begins to move with an acceleration of $1\,m{s^{ - 2}}$ . A man who is 48 m behind the bus starts running at $10\,m{s^{ - 1}}$ catch the bus. The man will be able to catch the bus after

A particle moves with constant acceleration and ${v_1},{v_2}$ and ${v_3}$ denote the average velocities in the three successive interval ${t_1},{t_2}$ and ${t_3}$ of time. Which of the following relations is correct?

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

A body starts from rest, with uniform acceleration. If its velocity after n seconds is v,then its displacement in the last two seconds is

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

A ball from height $h$ . After 1 second another ball falls freely from a point 20 m below the point from where the first ball falls. Both of them reach the ground at the same time what is the value of $h$ .

A train travelling with an initial velocity $u$ begins to decelerate uniformly. After travelling 500 m, its velocity becomes $\frac{u}{2}$. How much further will it travel before coming to a complete stop?