List of top Physics Questions on Kinematics asked in IPU CET

A particle moves in one dimension. Its velocity is given by \( v(t) = c_2 t^2 + c_1 t + c_0 \) where \( c_1 \) and \( c_2 \) are constants. What is the acceleration of the particle at time \( t = 1 \)?
Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction, with A ahead of speed B. The driver of B decides to overtake A and accelerates by 1 m/s². If after 50s, the guard of B just brushes past the driver of A, what was the original distance between them?
A train accelerates from rest at a constant rate $\alpha$ for distance $X_1$ and time $t_1$. After that it retards to rest at constant rate $\beta$ for distance $X_2$ and time $t_2$. Then, it is found that
A ball rolls up a slope. At the end of three seconds its velocity is 20 cm/s, at the end of eight seconds its velocity is 0. What is the average acceleration from the third to the eighth second?
In a car race, car A takes a time less than car B at the finish and passes the finishing point with speed \( v \) more than that of the car B. Assuming that both the cars start from rest and travel with constant accelerations \( a_1 \) and \( a_2 \) respectively. So, the value of \( v \) will be