1. 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 traveled by the particle from t = 0 to t = ? seconds. (4 points)

Options:

a) 2

b) 1

c)1/2

d)0

2. A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec² is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.

What is the total distance the car travels in this 30-second interval?

You must show your working but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.