Solving Rotations Homework: Double Speed vs Halving Radius

[baobao11]

Homework Statement

A truck was driven around a circular track. Which would have a greater effect on the magnitude of its acceleration: moving to a track with half the radius or doubling the speed.
Show proof/sample calculations.

Homework Equations

I'm not quite sure but I went ahead and tried this equation:
a = v^2/R

The Attempt at a Solution

I tried plugging in numbers:
a = v^2/R
v= 15m/s
R = 100m
a= (15^2)/(100) = 2.25 m/s^2

doubled speed:
a= (30^2)/100 = 9 m/s^2

half radius
a = (15^2)/50 = 4.5 m/s^2

If I'm correct, doubling speed will affect the magnitude of the acceleration more than the halved radius, right?
Thank you so much!

 

[rock.freak667]

Yes that is correct since whatever factor you multiply the velocity by, becomes squared as well.

a=v²/r

if 'v' is replaced by 'kv', then a' = k² (v²/r) = k²a

 

[baobao11]

Yes that is correct since whatever factor you multiply the velocity by, becomes squared as well.

a=v²/r

if 'v' is replaced by 'kv', then a' = k² (v²/r) = k²a

thank you very much for confirming my answer!