A cart of initial mass moves along a frictionless horizontal track with speed

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A cart of initial mass

M_0

moves along a frictionless horizontal track with speed

v_0

. Starting at

t=0

, fine sand with negligible horizontal velocity relative to the ground pours vertically into the cart at a constant rate

r

(in

\text{kg/s}

). Neglect any sand loss after it lands. Which expression gives the cart's speed

v(t)

at time

t

? (a)

v(t)=v_0\dfrac{M_0+rt}{M_0}

(b)

v(t)=v_0 e^{-rt/M_0}

(c)

v(t)=v_0\dfrac{M_0}{M_0+rt}

(d)

v(t)=v_0\sqrt{\dfrac{M_0}{M_0+rt}}