Theory question 117
DynamicsA particle moves from point O along a straight line such that its acceleration at any time, t seconds is a = (4 − 2t)ms−2. At t = 0, its distance from O is 18 metres while its velocity is 5ms−1,
(a) At what time will the velocity be greatest?
(b) calculate the; (i) time; (ii) distance of the particle from O when the particle is momentarily at rest.
Show the model answer
Model answer
v = ∫(4 − 2t)dt = 4t − t2 + 5 (v = 5 at t = 0)
s = 2t2 − t3/3 + 5t + 18 (s = 18 at t = 0)
(a) v is greatest when a = 0: t = 2 s (v = 9 ms−1)
(b)(i) v = 0: t2 − 4t − 5 = 0, (t − 5)(t + 1) = 0, t = 5 s
(ii) s = 50 − 125/3 + 25 + 18 = 51⅓ m
Explanation
Integrate acceleration to get velocity and again to get distance, using the starting values for the constants.