$A$ car travels in a straight line along a road. Its distance $x$ from a stop sign is given as a function of $t$ by the equation $x(t) = \alpha t + \beta t^3$, where $\alpha = 2.0 \ m \ s^{-1}$ and $\beta = 0.01 \ m \ s^{-3}$. Calculate the average velocity of the car in the time interval $t = 2.00 \ s$ to $t = 4.00 \ s$. (in $m \ s^{-1}$)

The position of an object moving along the $x$-axis is given by $x = a + b t^2$,where $a = 8.5 \; m$,$b = 2.5 \; m s^{-2}$,and $t$ is measured in seconds. What is the average velocity between $t = 2.0 \; s$ and $t = 4.0 \; s$ (in $; m s^{-1}$)?

Is the statement "$A$ particle can have zero speed but non-zero velocity" true or false? Explain.

Give the difference between average speed and average velocity.

Explain clearly, with examples, the distinction between
$(a)$ magnitude of displacement over an interval of time, and the total length of path covered by a particle over the same interval.
$(b)$ magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval].
Show in both $(a)$ and $(b)$ that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].

Which information cannot be drawn from average velocity?