Question

Derive an equation of which show relationship between position and time,when an object moves with uniform acceleration

Answer 1

where u=initial velocity

t=time taken

a=acceleration

v = final velocity

s=displacement

then,

a=v+u/ t

so , v=u+at (first equation of motion)

Answer 2

This is second equation of motion.

S=ut+1/2at²

derivational proof..

Following is a v - t graph displaying constant acceleration. (Slope of the curve is constant)

Curve Constant

At t = 0 seconds, the particle’s velocity is u m/s.

At t = t seconds, the particle’s velocity is v m/s.

Area under the curve of v − t graph gives displacement.

Now,

S = Area of Rectangle + Area of Triangle

S = (u - 0) × (t - 0) + 1/2(v - u)(t - 0)

S = ut + 1/2(v - u)(t)

(Substituting v − u = at, from first equation of motion and rearranging the terms)

S = ut + 1/2at²

Hope it helps !!

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