This displacement of a particle during its motion is equal to half of the product of its instantaneous velocity and time. Show that the particle moves with a constant acceleration.

Explanation

Let the displacement be s, instantaneous velocity be v and the time be t.
From the given condition,
`s = (1)/(2)vt = (1)/(2)(ds)/(dt)t" ""or",(ds)/(s) = 2(dt)/(t)`
Integrating we get ,
`int(ds)/(s) = 2 int(dt)/(t)`
or,`" ""log"_(e)s = 2"log"_(e)t+"log"_(e)c`
[where c is the integration constant ]
`"log"_(e)ct^(2)`
`:. " " s = ct^(2)` ,
` v = (ds)/(dt) = 2ct,`
and acceleration = `(dv)/(dt)` = 2c = constant.