Theory question 114
Dynamics(a) A car is moving with a velocity of 10ms−1. It then accelerates at 0.2ms−2 for 100m. Find, correct to two decimal places the time taken by the car to cover the distance.
(b) A particle moves along a straight line such that its distance S metres from a fixed point O is given by S = t2 − 5t + 6, where t is the time in seconds. Find its: (i) initial velocity; (ii) distance when it is momentarily at rest
Show the model answer
Model answer
(a) 100 = 10t + 0.1t², so t² + 100t − 1000 = 0 and t = (−100 + √14 000)/2 ≈ 9.16 s.
(b)(i) v = 2t − 5; at t = 0, v = −5 ms⁻¹ (5 ms⁻¹ towards O).
(ii) v = 0 at t = 2.5 s: S = 6.25 − 12.5 + 6 = −0.25, i.e. 0.25 m from O on the other side.
Explanation
Momentarily at rest means v = 0.