For a particle projected vertically upwards under gravity travels equal distance during $5^{th}$ and $6^{th}$ second of its motion. Find its projection speed........$m/s$ $(g = 9.8\,m/s^2)$

A wheel of radius $1$ meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

The maximum possible acceleration of a train moving on a straight track is $10\ m/s^2$ and maximum possible retardation is $5\ m/s^2$ . If maximum achievable speed of train is $10\ m/s$ then minimum time in which train can complete a journey of $135\ m$ starting from rest and ending at rest, is .........$s$

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

A car starts from rest and travels with uniform acceleration $\alpha$ for some time and  then with uniform retardation $\beta$ and comes to rest. If the total travel time of the car  is $‘t’$, the maximum velocity attained by it is given by :-

A parachutist drops freely from an aeroplane for $10\,s$ before the parachute opens  out. Then he descends with a net retardation of $2.5\, m/s^2$. If he bails out of the  plane at a height of $2495\, m$ and $g = 10\, m/s^2$, hit velocity on reaching the  ground will be .......$m/s$