Question

If a particle starting from rest has an acceleration that increases linearly with time as a=2t, then the distance travelled in third second will be

Answer 1

Do check and tell.
Good luck

Answer 2

acceleration (a) = 2t

so acceleration is variable so we can't use equation of motion...

we have to use integration ..

we know that dv/dt = a

so =). dv /dt = 2t

=). dv = 2t dt

on integrating this expression...

=). v = t^2 ( because initial velocity is zero)

and we also know that :---

dx/dt = v

so. =). dx/dt = t^2

=). dx = t^2dt

on integrating from limit from 0 to 3

=). x =[ t^3 /3]

= ). x = 3^3/ 3 = 27 /3 = 9 ( distance travelled in 3 sec)

distance travelled in 2 sec = 2^3 /3 = 8/3

so distance travelled in 3rd sec..

= 9 - 8/3 = 19/3 = 6.33 ans