Question

please please help! A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec^2 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 velocity of the car when t = 6? You must show your work and include units in your answer.

Answer 1

42 ft/s

Explanation:

The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is (10+4)/2 = 7 ft/s^2, so the change in velocity is ...

(7 ft/s^2)(6 s) = 42 ft/s

The velocity of the car at t=6 is 42 ft/s.