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A particle moves along a horizontal line such that its position s = 2t^3 − 9t^2 + 12 t
− 4, for t 0.
Find all t for which the particle is moving to the right.
Find all t for which the velocity is increasing.
Find all t for which the speed of the particle is increasing.
Find the speed when t = .
Find the total distance traveled between t = 0 and t = 4.SOLUTION:
and .
Velocity v = 0 at t = 1 and t = 2, and:
Acceleration a = 0 at t = , and:
These signs of v and a immediately yield the answers, as follows:
The particle moves to the right when t < 1 or t > 2.
v increases when t >.
The speed |v| is increasing when v and a are both positive, that is, for t > 2,
and when v and a are both negative, that is, for 1 < t < .
The speed when t = equals |v| = |− | = .Figure N4–15