A particle moves along the positive x-direction such that its speed depends on position according to v = v0 - kx, where v0 and k are positive constants and v remains positive in the region considered. The acceleration of the particle as a function of position x is:
Options

Question

A particle moves along the positive x-direction such that its speed depends on position according to v = v0 - kx, where v0 and k are positive constants and v remains positive in the region considered. The acceleration of the particle as a function of position x is:

Options

G1 Physics · Accepted Answer

Using a = dv/dt = (dv/dx)(dx/dt) = v(dv/dx). Since v = v0 - kx, dv/dx = -k. Thus a = (v0 - kx)(-k) = k^2x - kv0. Hence, option B is correct.