A particle moves along a straight line and its velocity depends on time as `v = 3t - t^2.` Here, v is in `m//s` and t in second. Find
(a) average velocity and
(b) average speed for first five seconds.

Answer

A, B, C

Explanation

(a) Average velocity=
Displacement /Time =`(int_0^5 vdt)/5`
`=(int_0^5(3t-t^2)dt)/5`
`=-0.833 m//s`
(b) Velocity of particle=0 at `t=3s`
i.e, at 3s, particle changes its direction of
motion.
Average speed=(Total distance)/(Total time)
=((Distance from 0 to 3s)+(Distance from 3s to 5s))/Time
`d_(0-3)=int_0^3(3t-t^2)dt=4.5m`
`d_(3-5)=int_3^5(t^2-3t)dt=8.67m`
`:.` Average speed =`(4.5+8.67)/5`
`=2.63 m//s`