# Velocity of an object on an inclined plane

• Prabs3257

#### Prabs3257

Homework Statement
A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Relevant Equations
Work energy theorem
I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

#### Attachments

Homework Statement:: A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Homework Equations:: Work energy theorem

I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?

There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?
Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this

Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this

You'd need to post your working. I'm not sure if it's worth it, though.

You'd need to post your working. I'm not sure if it's worth it, though.
I did post an img of it in the ques

I did post an img of it in the ques
There's almost no working there at all. You have an expression for ##v(x)## that you haven't justified. Did you integrate the friction force down the slope?

PS It looks like you just mixed up a factor of ##\sqrt 2## at some point.

I did post an img of it in the ques

Here's a neat trick. Maximising ##v## is the same as maximising ##v^2##. That makes the differentiation easier.

There's almost no working there at all. You have a very simple expression for ##v(x)## that you haven't justified and is wrong in any case. Did you integrate the friction force down the slope?
Oh sorry i just forgot f was not constant and i integrated it now and got the correct ans thanks