For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 .

Question

a. when id the particle at rest ? when is particle moving forward ?
b. Find the total distance traveled by the particle in intervals [0,1] seconds and [1,2] seconds . which is larger and why ?
c. when was the particle speeding up ? slowing down ?

Answer 1

at rest when ds/dt = 0
speeding up when ds/dt > 0

distance traveled in [a,b] is s(b)-s(a)

So, plug and chug

Answer 2

oops.
moving forward when s' > 0
speeding up when s" > 0