Question

a jogger whose mass is 60 kg is moving at a speed of 3 m/s. use the equation to find the joggers kinetic energy. ke = 1/2 mv² (60 kg)(3 m/s)² 1/2 (60 kg)(9 m²/s²) 1/2 (540 kgm²/s²) 4. explain look at the problem about the jogger. why does (3 m/s)² become (9 m²/s²)?

Explanation:

Step1: Identify the kinetic - energy formula

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the velocity.

Step2: Substitute the given values

Given $m = 60\ kg$ and $v = 3\ m/s$. Substitute into the formula: $KE=\frac{1}{2}(60\ kg)(3\ m/s)^{2}$.

Step3: Calculate $(3\ m/s)^{2}$

According to the exponent rule $(a\times b)^n=a^n\times b^n$, $(3\ m/s)^{2}=3^{2}\times(m/s)^{2}=9\ m^{2}/s^{2}$.

Step4: Calculate the kinetic energy

$KE=\frac{1}{2}(60\ kg)(9\ m^{2}/s^{2})=(30\ kg)(9\ m^{2}/s^{2}) = 270\ J$ (since $1\ J=1\ kg\cdot m^{2}/s^{2}$).

Answer:

$270\ J$