The position $x$ of a particle at any time $t$ is given by $x(t) = 4t^3 - 3t^2 + 2$. The acceleration and velocity of the particle at $t = 2 \, s$ are respectively:

The velocity-time graph of a body is shown in the figure. It implies that at point $B$

The figure shows the position of a particle moving on the $x$-axis as a function of time.

$A$ batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graphs describes the variation of the cricket ball's vertical velocity $v$ with time between the time $t_1$ as it hits the bat and time $t_2$ when it touches the ground?

We have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?