A particle travelled ${\left( {\frac{3}{4}} \right)^{th}}$ of the circle of radius R in time t. The magnitude of the average velocity of the particle in this time interval is

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 car starts from rest and moves with uniform acceleration a on a straight road from time t=0 to t=T. After that, a constant deceleration brings it to rest. In this process the average speed of the car is

A bullet travelling horizontally looses ${\frac{1}{{20}}^{th}}$ of its velocity while piercing a wooden plank. Then the number of such planks required to stop the bullet is

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is ${S_1}$ and that covered in the first 20 seconds is ${S_2}$ , then

Percentage of total distance covered in 5th Second by a freely falling body is

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.

If ${S_n} = 2 + 0.4n$, find initial velocity and acceleration $\left[ {{\rm{in}}\,\,{\rm{units}}} \right]$

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?

A bus moves over a straight level road with a constant acceleration a. A body in the bus drops a ball outside. The acceleration of the ball with respect to the bus and the earth are respectively

A car travels half the distance with constant velocity of 40 kmph and the remaining half with a constant velocity of 60 kmph. The average velocity of the car in kmph is