Question

A driver varies the speed of the car proportional to the square root of the time taken. Is the speed of the car during forward motion a linear or a nonlinear function of the time taken?

• A. The given data is insufficient.
• B. Linear function
• C. The given relation is not a function.
• D. Nonlinear function

Answer 1

The correct option is D Nonlinear function

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

The speed of the car is proportional to the square root of the time taken.
$\Rightarrow v\left(t\right)\propto \sqrt{t}$
$\Rightarrow v\left(t\right)=k\sqrt{t}$ ………….(Where k is a constant of proportionality.)
$v\left(t\right)=k{t}^{\frac{1}{2}}$

Squaring both sides,
$\Rightarrow v^2=k^{2}t$
$\Rightarrow t=\frac{1}{k^2}{v}^2$
Speed cannot be negative if the car is in forward motion.
The graph of the relationship is as follows:


Thus, the speed of the car is a nonlinear function of the time taken.