Question

A body moving along a given path has a displacement as a function of time given by 5t^2-7t-8 calculate the time it will come to rest

Answer 1

x=5t^2-7t-8

dx/dt=10t-7

v=10t-7

when it will come to rest then velocity become 0

so put this value in v=10t-7


0=10t-7

t=0.7sec

Answer 2

When it comes to rest, its velocity will be 0.

$displacement, \: x = 5 {t}^{2} - 7t - 8$

$velocity = \frac{dx}{dt} = 10t - 7$

$v = 0 \\ \\ 10t - 7 = 0 \\ \\ 10t = 7 \\ \\ t = \frac{7}{10} = 0.7s$

It will come to rest in 0.7 seconds.