Question

The motion of a body is given by the equation dv/dt=6.0-3v, where v is speed in m/s and t is in second. If body was at rest at t=0, then

Answer 1

Only option (d) is correct ie. the speed is 1.0 m/s when the acceleration is half the initial value.

Explanation:

(A) 

(B) The terminal speed is the constant speed when acceleration is zero. Thus 

0 = 6.0-3v

v = 2 m/s

(C) At t=0, v=0; therefore initial acceleration a = 6.0-0 = 6.0 m/s²

(D) Acceleration is half that of initial value = 6.0/2 = 3.0m/s²

This gives 3 = 6-3v(t)

or v(t) = 1m/s