Question

derive Newton's first equation of motion​

Answer 1

since....

a = dv/dt

●●●>>> a. dt=dv

..on applying limits

..●●>> at=[dv]^v_u...

●●>>>>v-u =at

Answer 2

Question-

Derive the first equation of motion.

Answer-

Assuming that a body started with initial velocity “u” and after time t it acquires final velocity v due to uniform acceleration a.  

We know acceleration is defined as the rate of change of velocity, also which is given by the slope of the velocity-time graph.

Thus both from definition as well as graph  Acceleration = Change in velocity/Time Taken i.e. a = v-u /t or at = v-u

Therefore, we have: v = u + at