Theory question 115
Dynamics(a) A boy runs in a line and his displacement at time t seconds after leaving the start point O is X metres, where 20X = 4t2 + t3. Find the: (i) velocity of the boy when t = 15 seconds; (ii) value of t for which the acceleration of the boy is 8 times his initial acceleration. (b) A body of mass 6 kg moves with a velocity of 7 ms−1. It collides with a second body moving in the opposite direction with a velocity of 5 ms−1. After collision, the two bodies move together with a velocity of 4 ms−1. Find the mass of the second body.
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(a) X = (4t² + t³)/20, so v = (8t + 3t²)/20 and a = (8 + 6t)/20.
(i) t = 15: v = (120 + 675)/20 = 39.75 ms⁻¹.
(ii) Initial acceleration = 8/20 = 0.4; 8 × 0.4 = 3.2 = (8 + 6t)/20, so 6t = 56 and t = 9⅓ s.
(b) 6(7) + m(−5) = (6 + m)(4), so 42 − 5m = 24 + 4m and m = 2 kg.
Differentiate displacement for velocity, and again for acceleration.