Question

derive first equation of motion from velocity time graph of an object​

Answer 1

Derive the first equation of motion v = u + at, using the velocity- time graph for a body moving along a straight line with uniform acceleration.

Answer 2

Explanation:

Figures shows the change in velocity with time of a uniformly accelerated object. Object starts from the point in the graph with velocity u. Its velocity keeps increasing and after time t,it reaches the point B on the graph.

the initial velocity of the object = u = OD

The final velocity of the object = v = OC

Time = t = OE

Acceleration (a)= change in velocity

Time

=(Final velocity - Initial velocity

Time

=(OC - OD)

t

therefore, CD = at .......(1) (OC - OD = CD)

draw a line parallel to y axis passing through B. This will cross the x axis in E.

draw a line parallel to x axis passing through D. this will cross the line BE at A.

From the graph..... BE= AB + AE

:. v= CD+ OD..... ( AB = CD and AE = OD)

:. v= at + u................ ( from 1)

:. v = u + at

This is the first equation of motion