Question

Derive the following equations of motion:
v = u + at
s = ½(u + v)t

Answer 1

Answer:

v = u + at ….

Which is First equation of motion ….

So , to derive it I am going to use Integration method ….

In the equation v = u+ at ….

v = final velocity

u = initial velocity

a = acceleration

t = time period of acceleration

Here we should note that acceleration is constant ….

At t = 0, initial velocity = u = OA  

At t = t, final velocity = v = OC

The distance S travelled in time t = area of the trapezium OABD

s = (1/2) x (OA + DB) × OD

s = (1/2) x (u + v) × t  

Since v = u + at,

s = (1/2) x (u + u + at) × t

s = ut + (1/2) at2  

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