Question

Derive th e equation of motion.
S = ut+ `1/2` at^2,
Where the symbols have their usual meanings

Answer 1

In figure we know
S = area of trapezium OSQP
Area of trapezium OSQP = 1/2 (sum of parallel sides) x perpendicular distance between them.
S = 1/2 (OP + SQ) x PR.
PR= QR/a= (QS-RS) / a
PR= (v - u)/a = t
So PR= t .
Substituting these values in expression of area of trapezium we get
S= 1/2 (u + v) xt
S = 1/2 (u +v) x (u - v)/a.
2aS = v2 - u2
v2 - u2 = 2 as.
This is known as third equation of motion.