Question

How fast would the car need to go to double its kinetic energy?

Answer 1

Answer:

Explanation:

Assume:

Given:

Kinetic energy, E2 = 2 × E1

But E = 1/2 × M × v^2

Where,

M = Mass

v = velocity

E2 = 2 × E1

= 2 × 1/2 × M × v1^2

E2 = M × v2^2. ......1

E1 = 1/2 × M × v1^2. .......2

Equating equation 1 and 2 to find the final velocity, v2:

1/2 × M × v1^2 = M × v2^2

2 × v2^2 = v1^2

v2^2 = v1^2/2

v2 = v1/sqrt(2)

Answer 2

Answer:

$v_{f} = \sqrt{2}\cdot v_{o}$

Explanation:

Let consider a car travelling at a speed $v_{o}$. The ratio of final kinetic energy to initial kinetic energy:

$\frac{\frac{1}{2}\cdot m \cdot v^{2}_{f} }{\frac{1}{2}\cdot m \cdot v^{2}_{o}} = 2$

$\frac{v_{f}}{v_{o}} = \sqrt{2}$

The final speed is:

$v_{f} = \sqrt{2}\cdot v_{o}$