Question

Derive the velocity-position equation of motion (v2=u2+2aS) graphically (with the help of a velocity-time graph).

Answer 1

Answer:

need to read an explained answer.

Explanation:

Velocity–Time graph to derive the equations of motion.

We have just seen that the distance travelled s by a body in time t is given by the area of the figure OABC which is a trapezium.

In other words,

Distance travelled, s = Area of trapezium OABC

Distance travelled =Area of trapezium

Now, OA + CB = u + v and OC = t.

Putting these values in the above relation, we get

------- (7)

We now want to eliminate t from the above equation.

This can be done by obtaining the value of t from the first equation of motion.

Thus, v = u + at (First equation of motion)

And, at = v – u or  

Now, putting this value of t in equation (7) above, we get:  

or 2as = v2 – u2 [because (v + u) × (v – u) = v2 – u2]

or v2 = u2 + 2as

This is the third equation of motion.