A velocity–time graph of a particle moving along a straight line is a smooth curve.
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A velocity–time graph of a particle moving along a straight line is a smooth curve.
(i) Define average acceleration of the particle between two instants t1 and t2 in terms of the graph.
(ii) Describe the graphical steps required to obtain the instantaneous acceleration at an instant t0. Explain why the slope of the tangent at the point (t0,v0) on the curve equals this acceleration.
(iii) Draw a small, neat sketch of a curved v–t graph and, on the same sketch, show a tangent at t=t0 as well as a chord joining (t0−Δt,v1) and (t0+Δt,v2). Using this sketch, justify why the chord gives an average acceleration over the interval 2Δt, whereas the tangent gives the exact instantaneous value at t0. State what happens to the average value as Δt→0.