Two battery-powered carts, Cart A of mass m and Cart B of mass 2m, sit at rest on a straight, level, nearly frictionless track. At the same instant each cart’s motor is switched on, and each motor delivers the same constant mechanical power P to its respective cart.
a. Describe qualitatively how the speed of each cart varies with time during the first few seconds after the motors are switched on.
b. At a generic instant t, determine the ratio vBvA of the speeds of the two carts in terms of their masses.
c. At the instant when Cart A has traveled a distance d, determine the speed of Cart B in terms of d, P, and m.
d. Explain why the accelerations of the two carts change differently over time even though the motors supply the same power.