A particle starts from rest with acceleration

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A particle starts from rest with acceleration ff. After time tt, the acceleration becomes 2f2f; after time 2t2t, it becomes 3f3f; and so on (it increases by ff every interval of length tt). (1) the speed at time ntnt (2) show that the distance covered in time ntnt equals [n(n+1)(2n+1)/12]f⋅t2[n(n+1)(2n+1)/12]f \cdot t^2

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