If a car of mass 1000kg travels up a slope inclined at 5 degrees at a speed of 20 meters per second calculate the power output of the car's engine (assuming a resistive force due to friction of 500N)

To find power we are going to need the equation:

P = F v 

Where P is power, F is force and v is velocity

Since the car is travelling at a constant speed up the slope, we know that velocity, v is positive 20 meters per second.

The next step is to determine the force.

In mechanics it is important not to overlook any forces (or components of forces) that might be acting. 

We must consider the force due to gravity and the resistive force due to friction as counterpoints to the driving force of the engine.

First, considering the force due to gravity:

 We must resolve parallel to the plane of the slope, in order to determine the force against which the engine works. This is done by taking the product of mass and the acceleration due to gravity, mg, to find the weight: 1000*9.81 = 9810 Newtons and then resolving parallel with sin(5), giving 1000*9.81*sin(5) = 855 (rounded).

Knowing the force due to friction as 500 Newtons, we sum to get F = 855 + 500 = 1355

With our original equation P = F v we have:

P = 1355 * 20 = 27.1 kW

Sam W. A Level Maths tutor, GCSE Maths tutor, A Level Further Mathema...

5 months ago

Answered by Sam, an A Level Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered: Further Mathematics , Physics+ 1 more

Further Mathematics

“Hi, my name is Ellie and I am currently studying Mathematics at the University of York. I chose York because I felt a real connection with the teachers, they made maths fun, interesting and easy. That's what I hope to do with all my s...”

MyTutor guarantee

£20 /hr

Tom M.

Degree: Maths (Bachelors) - Durham University

Subjects offered: Further Mathematics , Physics+ 2 more

Further Mathematics

“Who am I? Hi! My name is Tom and I am currently on a gap year heading off to Durham next year to study Maths. Ever since I can remember maths has been my favourite subject and I loved the problem solving that comes with it. When in my...”

MyTutor guarantee

£26 /hr

Lloyd S.

Degree: Mathematics G100 (Bachelors) - Bristol University

Subjects offered: Further Mathematics , Maths

Further Mathematics

“About Me:I am 19 and from Devon, currently in my first year studying Maths at the University of Bristol. I have a real passion for Maths and I really hope I can help you to understand, and maybe even enjoy doing maths - I know not ev...”

About the author

Sam W.

Currently unavailable: for new students

Degree: MSci Physics (Masters) - University College London University

Subjects offered: Further Mathematics , Physics+ 1 more

Further Mathematics

“I am a final year Physics MSci student studying at University College London, where I have achieved a first class in my first three years. Seeing my tutees learn and achieve their academic goals has been an incredibly emotionally rewa...”

You may also like...

Other A Level Further Mathematics questions

Why does e^ix = cos(x) + isin(x)

if y = (e^x)^7 find dy/dx

How do I use proof by induction?

Find the modulus-argument form of the complex number z=(5√ 3 - 5i)

View A Level Further Mathematics tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss