# Finding kinetic energy and initial velocity of a cart over time

• amelia2222
In summary: But you should set it up like this:In summary, based on the given information, the equation for this problem can be determined using the Work-Energy Theorem, which states that the net work is equal to the change in kinetic energy. Using this equation, we can solve for the final kinetic energy by subtracting the initial kinetic energy from the net work. This results in the equation: W=KEf-KEi. To find the final velocity, we can rearrange the equation to solve for vf and plug in the given values for mass and initial velocity. The final equation would be: vf=√(2W/m) where W is the net work (in this case, 4500J) and m is the
amelia2222
Homework Statement
During a period of time, a 100kg cart’s KE doubles. During that time, friction does -500J of work and the vehicle that is pulling the cart does 5000J of work on the cart. This scenario occurred on level ground. Find the final kinetic energy of the cart and the cart’s initial velocity
Relevant Equations
Worknc + KEinitial = KEfinal +Workfriction
Energy(initial) = Energy(final)
-I think there’s a equation for the initial velocity, but I’m not quite sure
Here's my list of variables and things to account for:
m=100kg
Wnc=5000J
Wfriction=-500J
-Kinetic energy will be doubled (though I don't know how that plays into it exactly)
-I don't think there's any PE because it's on level ground

My idea of what the equation might be:
Wnc +1/2mv^2initial = 2(1/2mv^2final) + Wfriction
5000+ 1/2(100)v^2 = 2(1/2(100)v^2) + 500

-From here, I'm not quite sure how to find both velocities and subsequently the final KE

Last edited:
Hello @amelia2222 ,
That's not enough to get started. It probably isn't enough for PF to allow assistance (see guidelines).
Perhaps you want to set up a list of variables involved (##t_0,\ t_1,\ v_0,\ v_1, \ ## etc.) where the 0 is for initial and the 1 for final.
And link them to the ones you have already (like ##KE_0 = {1\over 2} mv_0^2\ ## etc).

Don't forget the friction loss.

##\ ##

berkeman
BvU said:
Hello @amelia2222 ,
That's not enough to get started. It probably isn't enough for PF to allow assistance (see guidelines).
Perhaps you want to set up a list of variables involved (##t_0,\ t_1,\ v_0,\ v_1, \ ## etc.) where the 0 is for initial and the 1 for final.
And link them to the ones you have already (like ##KE_0 = {1\over 2} mv_0^2\ ## etc).

Don't forget the friction loss.

##\ ##
Thanks so much! I edited the section with my work in it, and I think it fits the guidelines now? I'm not quite sure

amelia2222 said:
Thanks so much! I edited the section with my work in it, and I think it fits the guidelines now? I'm not quite sure
Do you know the Work - Energy Theorem? (That's a hyphen, not a minus sign.)

I agree with @SammyS, you need to review and understand the Work - Energy theorem. In addition, you need to understand what Wnc is all about, how it differs (if it does) from Wfriction and where the 5000 J fits in all this.

SammyS said:
Do you know the Work - Energy Theorem? (That's a hyphen, not a minus sign.)
I think I do, that's the equation that the net work equals the change in kinetic energy correct? If that applies in this case, does that mean that I'd use this equation for this problem: W=KEf-KEi

Would the equation be set up like this: 4500J=2(1/2(100)v^2)-1/2((100)v^2)

Thanks for the guidance!

BvU
That would be correct.

## 1. How do you find the kinetic energy of a cart?

The kinetic energy of a cart can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the cart and v is the velocity of the cart.

## 2. What is the initial velocity of a cart?

The initial velocity of a cart is the speed at which it starts moving. This can be determined by measuring the distance the cart travels in a certain amount of time and using the formula v = d/t, where d is the distance and t is the time.

## 3. How can you measure the velocity of a cart over time?

The velocity of a cart can be measured using a motion sensor or by recording the distance the cart travels in a certain amount of time and calculating the velocity using the formula v = d/t.

## 4. What factors can affect the kinetic energy and initial velocity of a cart?

The mass of the cart, the surface it is traveling on, and the amount of force applied to the cart can all affect its kinetic energy and initial velocity.

## 5. Can the kinetic energy of a cart change over time?

Yes, the kinetic energy of a cart can change over time as its velocity changes. If the cart is accelerating or decelerating, its kinetic energy will increase or decrease accordingly.

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