A particle moves along a line with a velocity v(t)=t2−t−6, measured in meters per second. Find the total distance the particle travels from t=0 seconds to t=4 seconds.

10.67 m

Step-by-step explanation:

Velocity is given as;

v(t) = t² − t − 6

To get the distance, we will integrate the velocity equation.

x(t) = ∫v(t) = (t³/3) - (t²/2) - 6t

Thus, from t=0 seconds to t=4 seconds., we have;

(t³/3) - (t²/2) - 6t between 0 and 4.

Thus;

Total Distance = [(4³/3) - (4²/2) - 6(4)] - [(0³/3) - (0²/2) - 6(0)]

Total distance = (64/3) - 8 - 24 = -10.67 m

Distance can't be negative and so we take the absolute value which is 10.67 m