Variable acceleration?

During braking the speed v ms-1 of a car at time t seconds is modelled by v=75−3t^2 until it stops moving.

From the time when braking begins, the distance that the car travels before it stops is ___m

1 Answer
Apr 20, 2018

The distance is #=250m#

Explanation:

The car stops moving when

#v(t)=0#

That is,

#v(t)=75-3t^2=0#

#3t^2=75#

#t^2=25#

#t=5s# #" keeping only the positive value"#

The distance travelled is the integral of the velocity

#s(t)=int_0^5(75-3t^2)dt#

#=[75t-t^3]_0^5#

#=(75*5-125)-(0)#

#=250m#