Question

The law of motion in a straight line is given bys=1/2vt where v is the velocity at time t at a distance s from a fixed point on the linw. prove that the acceleration is constant.

Answer 1

1) Replace s by x .

x = 1/2 v t
x = 1/2 (dx/dt) *t
2dt/t = dx/x
2ln| t | = ln |x| + C where C is arbritrary constant

x = t^2 -C


2) Using above equation
dx/dt = 2t
v = 2t
dv/dt = 2
a = 2 which is constant .


Hence proved.

Answer 2

2 is the correct answer