Kinematics: UAM question help finding final velocity?

[ebuwsu]

Homework Statement

Can you use the UAM equation Vavg = x/t to solve for final velocity of a cart at the bottom of a ramp only using known x and time values before/without calculating for acceleration?

These are my values:

Xi = 0m
Xf = 2.27m
Vi = 0 m/s
Vf = ?
A = ? (can only use x and t values for this question)
t = 3.46s

It was explained that it could be used as an intermediate step to find final velocity, but then what equation do you use? I also don't quite understand how because the equation uses average velocity, so when I write it out and solve for Vf I am only solving for average final velocity, right?

Relevant Equations

Vavg = x/t = 1/2(Vi + Vf) = x/t

x

 

[PhanthomJay]

Homework Statement:: Can you use the UAM equation Vavg = x/t to solve for final velocity of a cart at the bottom of a ramp only using known x and time values before/without calculating for acceleration?

These are my values:

Xi = 0m
Xf = 2.27m
Vi = 0 m/s
Vf = ?
A = ? (can only use x and t values for this question)
t = 3.46s

It was explained that it could be used as an intermediate step to find final velocity, but then what equation do you use? I also don't quite understand how because the equation uses average velocity, so when I write it out and solve for Vf I am only calculating for average final velocity, right?
Relevant Equations:: Vavg = x/t = 1/2(Vi + Vf) = x/t

When you solve for the final velocity, that is not the average final velocity, it is the instantaneous final velocity after 3.46 seconds at x= 3.27 m. X is measured along the incline. What do you mean by average final velocity??

 

[ebuwsu]

Thank you for the clarification. I apologize I'm very new to physics, so I'm sure my statement is worded confusingly

The ultimate goal of the homework question is to determine whether or not I can use the average velocity UAM equation to solve for Vf with the known values. The explanation I was given in class was that you can use this equation as an intermediate step in conjunction with another UAM equation, but I don't understand how. What do I solve for in the average velocity equation that I can use in another equation to solve for Vf?

Hopefully, this makes more sense. I appreciate the help so late at night. I am stuck.

 

[haruspex]

Can you use the UAM equation Vavg = x/t to solve for final velocity of a cart ...

It was explained that it could be used as an intermediate step to find final velocity, but then what equation do you use?

For a straight ramp, the acceleration is constant. If you draw a velocity time graph, what relationship do you see between initial velocity, average velocity and final velocity?

 

[kuruman]

Yes you can as long as you know X_i, X_f, V_i and t. Starting from the relevant equation you posted, $$X_f-X_i=\frac{1}{2}(V_i+V_f)t$$ do a little bit of algebra to find $V_f$ in terms of the other quantities and then substitute the numbers. You don't need to mess with the average velocity $V_{ave}=\frac{1}{2}(V_i+V_f).$

 

[ebuwsu]

It’s an incline ramp. Sorry I should’ve specified that!

 

[ebuwsu]

2.27 - 0 = 1/2(0 + V_f)3.46

2.27 = 1/2V_f3.46

2.27 = 1.73V_f

2.27/1.73 = 1.73V_f /1.73

V_f = 1.31 m/s

Okay gotcha! So therefore this is my final velocity in the context of a cart rolling down an incline ramp and I can use the equation to find Vf. I think it just confused me that I was told it was supposed to be an intermediate step used along with a whole other equation.

 

[kuruman]

2.27 - 0 = 1/2(0 + V_f)3.46

2.27 = 1/2V_f3.46

2.27 = 1.73V_f

2.27/1.73 = 1.73V_f /1.73

V_f = 1.31 m/s

Okay gotcha! So therefore this is my final velocity in the context of a cart rolling down an incline ramp and I can use the equation to find Vf. I think it just confused me that I was told it was supposed to be an intermediate step used along with a whole other equation.

You can use the equation as you did to find the final velocity in cases where the acceleration is constant. The information that the cart is going down a straight ramp establishes that.

 

[ebuwsu]

Thank you for the clarification and verification!