Question

Using the attached graph, derive the
third equation of motion,
​

Answer 1

Answer:

Area of trapezium ABDOE = ½ x (Sum of Parallel Slides + Distance between Parallel Slides)

Distance (s) = ½ (DO + BE) x OE = ½ (u + v) x t … (3)

Now from equation (2): a=v−ut,

∴ t=v−ua … 4

Now, substitute equation (4) in equation (3) we get:

s=12(u+v)×(v−ua),

s = ½a (v + u) (v – u)

2as = (v + u) (v – u)

2as = v² – u²

v² = u² + 2as

This Expression gives the relation between position and velocity.