Question

The box having mass of m is being pulled by a motor. Initial velocity of the box is vy, Motor pulles the box by force F= 500s+550, where s is the distance the box is pulled (meters), and force is in newtons. Define the velocity and acceleration of the box as a function of distance 's'. If the motor has efficiency of e = 0.65, power input required to be supplied by the motor as a function of distance,

Answer 1

$a=\frac{F}{m}=\frac{500\times s+550}{m}$

Velocity looks like a function of distance and time, not distance only

$\upsilon=\upsilon_{0}+a\times t=\upsilon_{0}+(\frac{500\times s+500}{m})\times t=\upsilon_{0}+\frac{500}{m}\times s\times t+\frac{500}{m}\times t$

$P_{input}=\frac{P_{mech}}{e}=\frac{F\times s}{e}=\frac{500\times s^2+550\times s}{e}$