Question

A particle of mass m falls a given distance z0 in time t0=√2z0/g and the distance travelled in time t is given by z=at+bt^2 where constants a and b are such that the time t0 is always the same.show that integration 0 to t0 L dt is an extremum for real values of coefficient s only when a=0 and b= g/2.

Answer 1

v=$\frac{dz}{dt}=a+2bt$

acceleration=$\frac{dv}{dt}=2b$

2b=g

b=g/2

as this is freefall hence the initial velocity is zero

v=0

a+2bt=0

a+2.b.0=0

hence a=0