- #1

rock.freak667

Homework Helper

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## Homework Statement

A car travels around a circular track having a radius of 300m such that when it is at point A, it has a velocity f 5m/s, which is increasing at the rate of [itex]\dot{v}=0.06t m/s^2[/itex]. Determine the magnitudes of the velocity and acceleration when it has traveled one-third the way around the track

## Homework Equations

n,t-coordinate system

[tex]a=\sqrt{a_t^2+a_n^2}[/tex]

[tex]a_n= \frac{v^2}{r}[/tex]

## The Attempt at a Solution

Since the radius r=300m, the total distance the car will travel is [itex]2 \pi r= 600\pi m[/itex]

So I want to find v and a when the distance = 200pi

Now at A, [itex]\dot{v}=a_t=0.06t[/itex]

Initially at A,t=0 and v=5

so

[tex]\int^{v} _{5} = \int^{t} _{0} 0.06t dt[/tex]

[tex]v=5+0.03t^2[/tex]

Thus

[tex]\int ^{s} _{0}= \int ^{t} _{0} (5+0.03t^2) dt[/tex]

[tex]s=5t+0.01t^3[/tex]

When [itex]s=200\pi[/itex]

[tex]200\pi=5t+0.01t^3[/tex]

Which I do not know how to solve since there is no rational root.

Was I going on the correct track?