Answer to Question #264249 in Physics for barley

Question

Scenario: A four-horse carriage is accelerating by 6 m/s every three (3) seconds, carrying a total load (including the carriage, the coach man, and the passengers) of 275 kg. If the carriage is traveling for 50 meters along the dirt highway, whose friction value is known to be 451 N,

1. How much work does the four-horse carriage exerted?

2. How many seconds does the four-horse carriage had to attain the power necessary for work?

3. How much kinetic energy does the carriage possess?

Answer 1

1 The work is

$$W=F_\text{net}d=mad=m\frac{\Delta v}{\Delta t}d,\\\space\\ W=275·\frac{6}{3}·50=27500\text{ J}.$$

2 The power is

$$t=\sqrt{2d/a}=\sqrt{2d/(\Delta v/\Delta t)}=7.07\text{ s}.$$

3 The kinetic energy is

$$K=\frac12 mv^2=\frac12m·2ad=m\frac{\Delta v}{\Delta t}d=27500\text{ J}.$$