# Magnitude of velocity and acceleration

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1. Feb 24, 2016

### JustDerek

• Member advised to use the homework template for posts in the homework sections of PF.
A car travels around a circular track with a radius of r=250m. When it is at point A then VA=5m/s which increases at a rate of a=(0.06t)m/s2. Determine the magnitude of its velocity and its acceleration when it is 1/3 around the track. My distance in this situation is obviously 524m.

Can anyone help please? I've seen numerous different answers but none of these are what I need. I've tried integrating it twice but this gives the value of t as a complex number which doesn't really help me.
Derek

2. Feb 24, 2016

### JustDerek

Been informed that no integration is needed but this leaves me lost as to how to solve the problem.

3. Feb 24, 2016

### Randy Beikmann

I think you're making this too hard. Without doing the problem for you, I'll say that you've been given an initial tangential velocity, a constant tangential acceleration, and a tangential distance. You can calculate the final tangential velocity from this. Now, you already knew the final tangential acceleration, and you can now calculate the final radial acceleration from the tangential velocity. Then find the vector magnitude of that acceleration vector.

4. Feb 24, 2016

### JustDerek

Hey thanks for looking at this. I'll have a look using the hints you gave and let you know the result.

5. Feb 24, 2016

### JustDerek

The main thing confusing me is that the acceleration is $0.06tm/s^2$ but I don't know the time and I'm unsure how to calculate it

6. Feb 24, 2016

### PeroK

How would you solve the problem if the track were straight?

7. Feb 24, 2016

### JustDerek

Isn't the magnitude in both directions though, the tangential and normal directions, which is why the question is a curve?

8. Feb 24, 2016

### PeroK

I assume you mean the magnitude of the "acceleration". You should read the question more carefully. Where does it say acceleration?

9. Feb 24, 2016

### JustDerek

It's in two parts. First it says to find the magnitude of the velocity at 1/3 of the way round the track. Once that is found it asks to find the magnitude of acceleration for the same distance. It actually gives acceleration as v with the dot above it so it gives $\dot{v}=0.06t^2$

10. Feb 24, 2016

### PeroK

Are you sure that's the question? How do you know that $v$ is the velocity vector and not the speed?

11. Feb 24, 2016

### PeroK

That says to me that $V_A$ is the speed, which increases at a rate of $a$.

Velocity, strictly speaking, doesn't increase, it changes. If $a$ were the magnitude of the acceleration, I would expect the question to say so.

12. Feb 24, 2016

### JustDerek

That's the question. You can't see the $\dot{v} on there but on the desktop version I assure you that you can #### Attached Files: • ###### Screenshot_20160224-132619.png File size: 42.5 KB Views: 61 13. Feb 24, 2016 ### PeroK It's poorly worded. It should say speed, rather than velocity. In any case, if you really are given the magnitude of the acceleration as a constant, then Part B would be rather easy! 14. Feb 24, 2016 ### JustDerek But I need to find t I presume and then I can find the magnitude of velocity, but I'm not sure how to find t. The whole question is confusing. 15. Feb 24, 2016 ### PeroK Assume my interpretation. You know the speed, you know the increase in speed, you know the distance ... 16. Feb 24, 2016 ### JustDerek I'm still struggling but I don't want to try your patience anymore and I appreciate you taking the time to help greatly. 17. Feb 24, 2016 ### PeroK If you understand 1D kinematics, can you relate that to motion in a circle (or any other curve) if you are given the speed along the curve, the increase in speed along the curve and the distance along the curve? 18. Feb 24, 2016 ### JustDerek But all I know is that the increase in speed is$0.06*t## surely I need to know t before o can find the rest? Sorry I'm doing this degree after an 8 year break since I did the first year of dynamics. Sometimes a question pops up I just can't get my head around and then I have the "oh of course it is" moment ages later

19. Feb 24, 2016

### jbriggs444

Point A appears to be the starting point for the exercise. A reasonable assumption is that t=0 when the car passes point A.

20. Feb 24, 2016

### PeroK

So, you have a variable rate of increase in speed. Do you know how to handle that in 1D?