Kinetic Energy

#287 / Dynamics Medium

A 10 kN motorcycle is traveling at 100 kilometers per hour. What is its kinetic energy in kJ?

Expand Hint

$$$Force=mass\times acceleration$$$

Hint 2

Kinetic Energy:

$$$KE=\frac{1}{2}mv^2$$$

where $$m$$ is the mass and $$v$$ is the velocity.

In the problem statement, the weight of the motorcycle is given as a force. To find the mass:

$$$F=m\times a$$$

where $$F$$ is the force, $$m$$ is the mass, and $$a$$ is the acceleration due to gravity. Thus,

$$$10kN=m\times 9.81\frac{m}{s^2}$$$

$$$m=\frac{10,000kg\cdot (m/s^2)}{9.81m/s^2}=1,019.37\:kg$$$

Next, convert the velocity into meters per second:

$$$100 \frac{km}{hr}\cdot \frac{1,000m}{km}\cdot \frac{hr}{60min}\cdot \frac{min}{60s}=27.78\:m/s$$$

Finally, to solve for Kinetic Energy:

$$$KE=\frac{1}{2}mv^2$$$

where $$m$$ is the mass and $$v$$ is the velocity.

$$$KE=\frac{1}{2}(1,019.37kg)(27.78m/s)^2=393,338\:kg\cdot \frac{m^2}{s^2}$$$

$$$=393,338N\cdot m=393\:kJ$$$

393 kJ

Time Analysis

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