A cart has mass 2 metric tone and sand of 1 metric tone is inside the cart. Now a force of 10 ~N is applied on cart and sand starts to leak with rate of 0.5 ~kg / s . What is the velocity of cart when total sand has come out from the cart?

Step-by-step solution

Mass of the cart with sand changes then its acceleration also changes. a= F m = F m₀- t where m is mass of system at time t , aligned & m=m₀- t & a= F m₀- t or d v d t = F m₀- t aligned aligned & ₀^v d v=F ₀^t d t m₀- t & v= F ( m₀ m₀- t ) aligned Here F=10 ~N ; =0.5 ~kg / s m₀=2 metric tone m₀- t=1 metric tone v= 10 0.5 (2)=20 0.693=13.86 ~m / s