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 can be the plot of acceleration against time
B. Curve 2 can be the plot of velocity against time
C. Curve 2 can be the plot of velocity against acceleration
D. Curve 1 can be the plot of displacement against time

Answer

A, B

Explanation

`a=F/m=alpha/mt……(i)`
or `apropt`
i.e. a-t graph is a straight line passing through
origin.
If `u=0,` then integration of Eq. (i) gives,
`v=(alphat^2)/(2m)` or `vpropt^2`
Hence in this situation (when `u=0`) v-t graph is a
parabola passing through origin.