Question

Draw a velocity-time graph of uniformly accelerated motion in one dimension. From the velocity-time graph of uniformly accelerated motion deduce the equations of motion in distance and time.

Answer 1

A graph drawn by taking time along x-axis and velocity along y-axis is called velocity-time graph. Consider a particle moving along a straight line with a constant acceleration ‘a’. Let u be its velocity at time t = 0 and v be the velocity after t seconds. The velocity-time graph AC of this particle is shown in the figure.

Distance travelled by the particle in t seconds is given by,

s = area under v-t graph

= area of the triangle ABC + area of the rectangle ABDO

= 1/2 BC × AB + OA × OD From the graph,

BC = CD – BD = v – u,

AB = OD = t and OA = u

∴ s = 1/2 (v - u) t + ut …….. (1)

But, a = Slope of the graph = (v - u)/t

∴ v – u = at

On substituting in (1) we have,

s = 1/2 at.t + ut

s = ut + 1/2 at².