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?
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
