Normal and Tangential Acceleration

1. Jan 29, 2013

aaronfue

1. The problem statement, all variables and given/known data

A motorcyclist travels around a curved path that has a radius of 450 ft. While traveling around the curved path, the motorcyclist increases speed by 1.10$\frac{ft}{s}$. Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.00 $\frac{ft}{s^2}$

2. Relevant equations

a = √(at)2+(an)2

at=$\dot{v}$
an = $\frac{v^2}{ρ}$

3. The attempt at a solution

I've already solved for the speed at a given acceleration, and the magnitude of the acceleration at a given speed.

But this part is a little confusing for me. I am thinking that I have to use the equation a = √(at)2+(an)2 and set a = 7.00 $\frac{ft}{s^2}$ and then I can solve for an.....then solve for v in the equation an = $\frac{v^2}{ρ}$, where ρ = 450 ft? But I'm not sure. I will give it a try, though.

If anyone can weigh in on my approach, I would greatly appreciate it as always!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 29, 2013

Simon Bridge

That's how I'd interpret the problem - the total acceleration would be the vector sum of the tangential and centripetal accelerations.

3. Jan 30, 2013

aaronfue

Thanks. Worked out fine.