Example+2+(homework+problem)



1. At t = 4 seconds, is the particle moving to the right or left? Explain your answer (Sam).

2. Over what time interval is the particle moving to the left? Explain your answer (Itai).

The particle will be moving to the left when the value of the velocity is less than 0. Therefore, the particle will be moving to the left after the value x=5.

3. At t = 4 seconds, is the acceleration of the particle positive or negative? Explain your answer (Maddie D)

At t=4 seconds, the acceleration of the particle is negative because the slope of the tangent line is negative at t=4 seconds.

4. What is the average acceleration of the particle over the interval [2, 4]? Show the computations that lead to your answer and indicate

units of measure. (Monica)

change in velocity/time interval = f(4)-f(2)/4-2 = 6-9/2 = -3/2 ft/s^2

5. Is there guaranteed to be a time //t// in the interval [2, 4] such that v ' (t) = -3/2 ft/sec? Justify your answer. (Mike B.)

no, because the slope is less than -3/2 from 3 to 5, and the average acceleration is not the same as v'(t) because the slopes signs. 6. At what time t in the given interval is the particle farthest to the right? Explain (Charles). at t=5. This is when the particle is the farthest to the right, because at t=5 the velocity changes sign. This means it is now going to the left.