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 are correct ?

Options

A. Curve `1` shows acceleration against time
B. Curve `2` shows velocity against time
C. Curve `2` shows velocity against acceleration
D. none of these

Answer

D

Explanation

`F=alphat`
`ma=alphat` `rArr aalphat`
curve 1 is against time `(mdv)/(dt) = prop t`.
Integrating this we get `v prop t` this implise parabola.
also `v prop a^(2)rArr ` curve 3 shows velocity against acceleration.