Theory question 114
DynamicsA particle of mass 2 kg moves under the action of a constant force, F N, with an initial velocity (3i + 2j) ms−1 and a velocity of (15i − 4j) ms−1 after 4 seconds. Find the: (a) acceleration of the particle; (b) magnitude of the force F; (c) magnitude of the velocity of the particle after 8 seconds, correct to three decimal places.
Show the model answer
Model answer
(a) a = (v − u)/t = (12i − 6j)/4 = 3i − 1.5j ms⁻².
(b) F = ma = 6i − 3j; |F| = √45 ≈ 6.71 N.
(c) v = u + at = (3i + 2j) + 8(3i − 1.5j) = 27i − 10j; |v| = √829 ≈ 28.792 ms⁻¹.
Explanation
Work with the i and j parts together as vectors.