Please help. __

Question

The velocity of a particle moving along the x-axis is v(t) = t2 - 2t, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = 3 minutes.

Answer 1

The trick here is that the displacement is simply the integral of V, and it will give you the answer = 0.

So the particle will return to the same point.

But the total distance - is an integral of absolute value of V.

So, we split the integral in 2 parts - where the V>0 and V<0

First, let's solve the inequality to see what these 2 integrals are

t^2-2t > 0

t*(t - 2) > 0

(0,2) V is negative and the formula for the absolute value of V will be 2t-t^2

(2,3) V is positive and the formule for the abs. value of V will be t^2-2t

So the answer will be:

∫₀²(2t-t^2) + ∫₂³(t^2-2t)