Question

A particle is moving along x-axis such that its velocity varies with time according to `v=(3m//s^(2))t-(2m//s^(3))t^(2)`. Find the velocity at t = 1 s and average velocity of the particle for the interval t = 0 to t = 5 s.

Answer 1

(i) `v=3t-2t^(2)`
`v_(1)=3xx1-2^(2)=-1m//s`
(ii) `v_(av)=(x_(5)-x_(0))/(5-0)." Now, "v=(dx)/(dt) rArr dx = vdt rArr int_(x_(0))^(x_(5))dx= int_(0)^(5)3tdt- int_(0)^(5)2t^(2)dt`
`rArr x_(5)-x_(0)=3((t^(2))/(2))_(0)^(5)-2((t^(3))/(3))_(0)^(5)=(75)/(2)-(250)/(3)`
`v_(av)=(x_(5)-x_(0))/(5-0)=-(275)/(5xx6)=-(55)/(6)m//s.`