The question is about Mechanics (so a mix of maths and physics)(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A car of mass 900kg moves along a straight horizontal road with its engine working at a constant rate of 20kW. Its speed at A is 10m/s, Assuming that there is no resistance to motion, calculate the time taken for the car the travel from A until its speed reaches 20ms.

u=10

v=20

P=20000

2. Relevant equations

[tex]\vec{F}_{net} = \Sigma \vec{F} = m \vec{a}[/tex]

3. The attempt at a solution

Firstly, I drew a diagram that looked similar to this: http://skrbl.com/130853849 (sorry, scanner broken!)

Power = Fv therefore F = 20000/v

FCA F=ma N2L

Res (->) (20000/v) = 960a

a = 125/6v

I know I need to integrate the acceleration formula (due to variable acceleration) but I'm not sure how to do with wrt t. My problem is because there is no t. I do remember my teacher saying something about integrating both sides to find time (school is over here now though so I can't get hold of him). I have attempted to integrate both sides but it still made little sense. I did a little browsing on these forums and came up with this though:

integral(dv) = integral([125/6v]dt)

I appreciate any and all help - it's probably something simple that I just can't see! I mainly need hints (would rather not answers) on how to integrate this to give me something in relation to time.

By the way, according to the textbook the answer is 7.2 seconds.

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# Homework Help: Work, Energy and Power - Variable Acceleration

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