Question

1. the kinetic energy ( e ) of a moving object is given by ( e=\frac{1}{2}mv^{2} ), where ( m ) is its mass in kilograms and ( v ) is its speed in meters/second.

6a if a vehicle traveling at ( 20 , \text{m/s} ) has kinetic energy ( e = 500000 ), what is the mass of the car?

Explanation:

Step1: Substitute the given values into the formula

Given \(E = 500000\), \(v = 20\), and the formula \(E=\frac{1}{2}mv^{2}\). Substitute these values: \(500000=\frac{1}{2}\times m\times(20)^{2}\).

Step2: Simplify the equation

First, calculate \((20)^{2}=400\). The equation becomes \(500000=\frac{1}{2}\times m\times400\). Then \(\frac{1}{2}\times400 = 200\), so \(500000 = 200m\).

Step3: Solve for \(m\)

Divide both sides of the equation \(500000 = 200m\) by \(200\). Using the formula \(m=\frac{500000}{200}\).

Answer:

\(m = 2500\) kilograms