Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    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. :confused:

    Any help appreciated!
    Offline

    2
    ReputationRep:
    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
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah I'd not clicked that at top speed there's no acceleration. Thanks, Jonny.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 11, 2006
Poll
Do you like carrot cake?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.