Question

A car starts from rest, accelerates uniformly for 4 seconds and then moves with a uniform velocity. Which of the following x-t graphs represents the motion of the car till t = 7 s?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Since the car starts from rest and has a uniform acceleration, say a, till t = 4s, the distance covered by the car during this time is given by
$x=\frac{1}{2}a{t}^2$
Since $x\propto t^2$, the x-t graph during first 4 seconds is a parabola with a slope (which gives velocity) increasing with time. After t = 4s, the velocity is uniform which means that the x-t graph should be linear with a positive slope. Option (d) is, therefore, the correct choice.