What is the Radius of Curvature at Point B on the Road?

[LeFerret]

Homework Statement

The speed of a car increases uniformly with time from 50km/hr at A to 100km/hr at B during 10 seconds.

The radius of curvature of the bump at A is 40m.

if the magnitude of the total acceleration of the car’s mass center is the same at B as at A, compute the radius of curvature of the dip in the road at B. The mass center of the car is 0.6m from the road.

Homework Equations

a_n=V_B²/ρ

The Attempt at a Solution

Before I solve this problem, I want to get some conceptual questions out of the way.
It says the magnitude of acceleration is constant, does this mean that the normal and tangential components of acceleration are constant from A to B?
If so can I just compute a_n=V_A²/ρ at A and use that for a_n at B?

 

[voko]

Total acceleration is not indicated to be constant. All that is said about total acceleration is that its magnitude is the same at A and B.

 

[LeFerret]

Total acceleration is not indicated to be constant. All that is said about total acceleration is that its magnitude is the same at A and B.

but velocity increases uniformly, wouldn't that imply that the tangential acceleration is constant?
and if tangential acceleration is constant, and the magnitude of acceleration at A and B are the same, then that must mean the normal acceleration at A and B are equal?

 

[voko]

Velocity is a vector, it cannot increase. The speed does increase uniformly, and that makes the rest of your reasoning correct.

 

[LeFerret]

Velocity is a vector, it cannot increase. The speed does increase uniformly, and that makes the rest of your reasoning correct.

Ah I see, so when computing normal acceleration at A, ρ is given to be 40meters from the curve, however since the center of mass of the car is .6meters from the surface, I would use V_A²/40.6 correct?

 

[voko]

Yes, that looks correct to me.

 

[LeFerret]

Yes, that looks correct to me.

Thank you for the help!