Please help thank you in advance

Question

A particle moves along the x-axis with velocity v(t) = sin(2t), with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = π seconds.

 2

 1

1/2

0

Answer 1

The integral of sin2t should be -0.5 cos(2t).

The travel should be adding the positive part from 0 to pi/2 , and the absolute value of the negative part from pi/2 to pi.

The answer is 2.

Answer 2

Well total distance travelled = integral of modulus of v(t) from t = 0 to t = π

Integrating modulus of v(t) gives 0.5 cos 2t [ differentiating 0.5 cos 2t gives sin 2t]

When t = π, 0.5 cos 2t = 0.5

When t = 0, 0.5 cos 2t = 0

so distance travelled = 0.5 - 0 = 0.5 ft