Question

Draw the velocity-time graph for a uniformly accelerated motion
and derive the first and second equations of motion with help of
this graph​

Answer 1

Answer:

A graph drawn by taking time along the x-axis and velocity along the y-axis is called a 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

=1/2BC×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−ut

∴ v – u = at

On substituting in (1) we have,

s=1/2at.t+ut

s=ut+1/2at

2

.

Answer 2

Answer:

A graph drawn by taking time along a x-axis and velocity along the y-axis is called a velocity -time graph.