If velocity (in `ms^(-1)`) varies with time as V = 5t, find the distance travelled by the particle in time interval of t = 2s to t = 4 s.

Options

A. 24 m
B. 30 m
C. 10 m
D. 20 m

Answer

B

Explanation

Here, V = 5t is given.
`therefore (dx)/( dt) = 5t (because V = (dx)/(dt))`
`therefore dx= 5t dt`
Taking integration `int _(20) ^(x) dz = 5 int _(2) ^(4) t dt`
`(because t = 2s ` to `t = 4s)`
`therefore x =5 [ (t ^(2))/( 2) ] _(2) ^(4) = 5 [8-2]`
`therefore x = 30,`