x Turn on thread page Beta
 You are Here: Home >< Maths

# mechanics 2, power watch

1. A car manufacturer plans to bring out a new model with a top speed of 64m/s to be capable of accelerating at 0.1m/s2 when the speed is 60m/s. Wind-tunnel tests on a prototype suggest that the air resistance at speed v m/s will be 0.2v² newtons. Find the power output (assumed constant) of which the engine must be capable at these high speeds, and the constraint which the manufacturer's requirement places on the total mass of the car and its occupants.

Any help appreciated!
2. Let

P = power produced by engine (a constant)
F = force produced by engine
m = car's mass (a constant)
v = car's speed
a = car's acceleration

Then

F = P/v

a
= (1/m) (F - 0.2v^2)
= (1/m) (P/v - 0.2v^2)

Since a = 0 when v = 64, P = 0.2(64)^3 = 52428.8.

Since a = 0.1 when v = 60, m = (52428.8/60 - 0.2(60)^2)/0.1 = 1538.1
3. Ah I'd not clicked that at top speed there's no acceleration. Thanks, Jonny.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 11, 2006
Today on TSR

### Complete university guide 2019 rankings

Find out the top ten here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams