Theory question 114
Dynamics(a) A particle initially at rest moves in a straight line with an acceleration of (10t − 4t2) ms−2. Find the: (i) velocity of the particle after t seconds; (ii) average acceleration of the particle during the 4th second.
(b) A load of mass 120 kg is placed on a lift. Calculate the reaction between the floor of the lift and the load when the lift moves upwards: (i) at a constant velocity; (ii) with an acceleration of 3 ms−2. [Take g = 10ms−2]
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(a)(i) v = ∫(10t − 4t²) dt = 5t² − (4/3)t³ (v = 0 at t = 0).
(ii) The 4th second is from t = 3 to t = 4: v(3) = 45 − 36 = 9; v(4) = 80 − 256/3 = −16/3.
Average acceleration = (v(4) − v(3))/1 = −16/3 − 9 = −43/3 ≈ −14.3 ms⁻².
(b)(i) R = mg = 1200 N. (ii) R − 1200 = 120 × 3, R = 1560 N.
The 4th second runs from t = 3 to t = 4.