Question

A go-kart and rider have a mass of 14 kg. If the cart accelerates at 6 m/s² during a 40 m sprint in 100 seconds, how much power did the cart do?

Answer 1

Answer:

P=33.6 \ W

Explanation:

Mechanical Work and Power

Work is the amount of energy transferred by a force. It's a scalar quantity, with SI units of joules.

Being $\vec F$ the force vector and $\vec s$ the displacement vector, the work is calculated as:

$W=\vec F\cdot \vec s$

If both the force and displacement are parallel, then we can use the equivalent scalar formula:

$W=F.s$

Mechanical Power is the amount of energy transferred or converted per unit of time. The SI unit of power is the watt, equal to one joule per second.

The power can be calculated as:

$\displaystyle P=\frac {W}{t}$

Where W is the work and t is the time.

If an object of mass m has an acceleration a, the net force is:

F=m.a

The go-kart and rider have a mass of m=14 kg and accelerate at $6 m/s^2$, thus the net force applied is:

$F=14\cdot 6 = 84\ N$

The work done by the cart when traveling d= 40 m is:

$W=84\cdot 40$

$W=3,360\ J$

Finally, the power for t= 100 seconds is:

$\displaystyle P=\frac {3,360}{100}$

P=33.6 \ W