s(t) = 2t^2 - 16t + 24 describes the position of an object. For 0 < t < 60, when is the object at rest? Assume t is seconds and the distance is in cm. Followup: When is the object moving at 48 cm/sec?

Answer 1

s(t) =2t^2 -16t +24

s'(t) = v(t) = 0 = derivative of 2t^2 -16t +24 = 4t-16,

when the object is at rest (for an instant, a super super micro second)

4t-16 = 0

t = 16/4 = 4 seconds to be at rest, momentarily

v(t) = 48 = 4t-16

4t = 64

t = 64/4 = 16 seconds for velocity to be 48 cm/sec