Question

A car racer is varying the speed of the car proportional to the square root of time. Is the speed of the car during the forward motion a non-linear function of time? Answer in Yes/No.

Answer 1

Here, time $t$ is the independent variable, and speed $v$ depends on the time of travel.

The speed of the car is proportional to the square root of time.
$\Rightarrow v\propto \sqrt{t}$
$\Rightarrow v=k\sqrt{t}$
where $k$ is a constant of proportionality.

Squaring both side,
$\Rightarrow v^2=k^{2}t$
$\Rightarrow t=\frac{1}{k^2}{v}^2$
Here, speed cannot be negative in the forward motion.
The plot of the relation is as follows:
This is a non-linear function.