Help with Calculus?

Question

The velocity function is v(t)=t^2−4t+3 for a particle moving along a line. Find the displacement and the distance traveled by the

particle during the time interval [-3,6].

Answer 1

The velocity function is v(t) = t² - 4t + 3 and time interval [-3, 6].

dx/dt = v(t) = t² - 4t + 3

dx = (t² - 4t + 3) dt

The displacement is 54.

Answer 2

(2).

Find the distance.

The velocity is positive or negative when v(t) = 0.

The intervals are [-3, 6] and [1, 3] and its order -3, 1, 3 and 6.

Velocity is positive in the interval [-3, 1] and [3, 6] and the velocity is negative in the interval [1, 3].

 

 

The distance is 170/3.