Question

(20 Points) Given a particle's position is x = -t^2 + 2t, find the total distance it travels over [0, 2].

Answer is 2 m.

Answer 1

t = 2 or t = 0

Explanation:

Solve for t over the real numbers:

2 t - t^2 = 0

Factor t and constant terms from the left hand side:

-t (t - 2) = 0

Multiply both sides by -1:

t (t - 2) = 0

Split into two equations:

t - 2 = 0 or t = 0

Add 2 to both sides:

Answer: t = 2 or t = 0