Question

Define uniform velocity obtain v² – u² = 2as from the v – t graph, where the symbols have the usual meaning.

Answer 1

If a body undergoes equal displacements in equal intervals of time, however small interval of time may be then velocity is said to be uniform velocity.

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 travelles by the particle is given by,

s = area under v-t graph

= area of the trapezium OACD

= 1/2 (OA + CD) × OD

But OA = u, CD = v and OD = t

∴ s = 1/2 (u + v) t or 2s = (u + v) t ………(1)

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

∴ t = (v - u)/a

On substituting in (1), 2s = (u + v)((v - u)/a)

i.e., v² – u² = 2as

or v² = u² + 2as.