Question

What is the velocity of a 16.3 kg car moving with 85 J of energy?

Answer 1

Velocity is 10.429 m/s

Step-by-step explanation:

Assume a car is moving from rest at point A to point B through a distance r.

We know that workdone is product of force and distance moved;

`{ \bf{ \triangle w = f \triangle r}}`

- Integrating both sides;

`{ \bf{ \int \triangle w = f \int^{r_(2)}_{r_(1) } \triangle r}} \\ \\ { \bf{w = (ma) \{r _(2) - r _(1) \}}} \\ \\ { \bf{w = (m * \frac{ {v}^(2) }{2r}) * (r) }}`

The step above comes from Newton's third law, where initial velocity is zero, since car is from rest, and r1 is zero

`{ \bf{w = (m * \frac{ {v}^(2) }{2}) * (r)/(r) }} \\ \\ { \boxed{ \rm{workdone = (1)/(2)m {v}^(2) }}}`

Therefore;

`{ \rm{85 = (1)/(2) * 16.3 * {v}^(2) }} \\ \\ { \rm{ {v}^(2) = (2 * 85)/(16.3) }} \\ \\ { \rm{v = \sqrt{( (2 * 85)/(16.3) } )}} \\ \\ { \rm{v = 10.429 \: ms {}^( - 1) }}`