Question

2.2*10^6J of work are needed to accelerate a 5700kg trailer trunk to 100 km/h. how fast would it go if 1/2 as much work were done on it?

Answer 1

Recall the 3 eqns:
1)
\[Work done =\frac{ force }{ distance }\]
Therefore work done is directly proportional to the force applied
`This means that in order to double the work done, double the force needs to be applied. Conversely to halve the work done, half the force needs to be applied (provided the distance covered is the same`

2)
\[Force=mass \times\ acceleration\]
Over here the force applied is directly proportional to the acceleration
`so just like before halving the force applied would halve the acceleration (provided mass remains constant)`

3)
\[acceleration = \frac{ v - u }{ t }\]
The time ''t in both cases is the same and initial velocity is zero
Now you can easily figure out the new final velocity
`Since the acceleration was halved and everything else remained the same, it follows that the only thing affected by halving the work done is the final velocity`

```
The final velocity would be half of 100 km/h
```