Question

A particle is resting over a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $F=\alpha t,$ where $\alpha$ is a positive constant. From figure, which of the following statements is(are) correct?

• A. Curve $1$ shows acceleration against time
• B. Curve $2$ velocity against time
• C. Curve $2$ shows velocity against acceleration
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A Curve $1$ shows acceleration against time
B Curve $2$ velocity against time

$F=ma=\alpha t$, thus $a\propto t$ or a-t curve is linear.
Hence Curve 1 can be acceleration-time curve.
Velocity should hence be quadratic, thus curve 2 can be $v-t$ curve.