Radial & Tangential Acceleration of a Car at Indianapolis 500 | Physics Solution

[y90x]

Homework Statement

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 200 m. Determine the tangential and radial acceleration of the car when it is halfway through the arc, assuming constant tangential acceleration. If the curve were flat, what coefficient of static friction would be necessary between the tires and the road to provide this acceleration with no slipping or skidding?



The attempt at a solution
I solved for tagental acceleration :
At= vf^2- Vo^2 /2d
= 88.8^2/2(pi * 200)
=6.288 m/s^2

For the radial acceleration is :
Ac= v^2/r
=88.8^2/200
=39.5 m/s^2
The correct answer is 19.75m/s^2
Why am I getting it wrong (the radial acceleration)? :/
88.8 is in m/s btw (from the 320 km/h)

 

[haruspex]

from the 320 km/h

from rest to 270 km h

?

 

[y90x]

?

That first one was a typo , in the paper it says 320 km/h

 

[haruspex]

when it is halfway through the arc

Did you read that correctly when you wrote:

Ac= v^2/r
=88.8^2/200

?

 

[y90x]

Did you read that correctly when you wrote:

?

That would mean the 200 m changes to 100 m
And it’ll give me a higher number , 79.03 m/s^2

 

[haruspex]

That would mean the 200 m changes to 100 m

No, the radius is 200m. But what velocity are you using in v²/r?

 

[y90x]

No, the radius is 200m. But what velocity are you using in v²/r?

Ohh, that’s the final velocity when it’s at the end of the arc ? So I find the velocity when it’s halfway , then apply it in v^2/r

 

[haruspex]

Ohh, that’s the final velocity when it’s at the end of the arc ? So I find the velocity when it’s halfway , then apply it in v^2/r

Yes.