Question

Displacement of an object is directly proportional to the square of the time elapsed. Choose all correct statements.

Motion is uniformly accelerated motion.

D – T graph of this motion is a straight line.

V –T graph of this motion is a straight line inclined to the axes

Velocity is directly proportional to the square of the time elapsed.

Answer 1

1. True. Let distplacement be $s = kt^2$ where $k$ is some constant. By definition, the acceleration is the second derivative of the displacement which is $a = 2k = const$.

2. False. D – T graph of this motion is a parabola because of $t^2$.

3. True. The velocity is the first derivative of the displacement, namely $v = 2kt$. This is the equation of a straight line inclined to the axes with the slope $2k$.

4. False. From the previous point, velocity is directly proportional to the time elapsed.