Question

If the velocity of a car on a timed test drive on an airfield is given by the function:

V= 24t - 3t(squared)
Where v is in m/s and t is in seconds
Starting from rest, the car comes to rest again after 8 seconds. How far has it travelled during that time?

Answer 1

The graph of the car's speed is a piece of an inverted parabola,
that cuts the time axis at zero and at 8 sec.

The distance the car travels during that 8 seconds is the area
between the parabola and the time axis. If you intend to calculate
it, then I'm afraid you're going to need to integrate the speed function.

V = 24t - 3t²

Distance = integral of (24t - 3t²), evaluated from zero to 8 seconds.

Integral of (24t - 3t²) =

t²/2 - 3t³/3 = 12t² - t³

Evaluated between zero and 8 seconds, the integral is

12(8²) - (8)³ =

768 - 512 = 256 meters .