Finding how long it takes for a_t to equal a_c

[klm_spitfire]

Homework Statement

A new car is tested on a 300-m-diameter track. If the car speeds up at a steady 1.3 m/s^2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

c = 300 m
a_t = 1.3 m/s^2

2. Relevant formulas

a_c = v^2 / r -- Centripetal Acceleration
t = (v_f - v_i) / a -- Time
r = c / 2π -- Radius

The Attempt at a Solution

[/B]
r = 300 / 2π = 150 / π
a_t = a_c = 1.3 = v^2 / (150 / π)
v = sqrt((150 / π) * (1.3))
t = (sqrt((150 / π) * (1.3)) - 0) / 1.3 = 6.06 seconds

This isn't correct though... It would appear the answer should be ~11 seconds. Help? Lol.

 

[ehild]

Homework Statement

A new car is tested on a 300-m-diameter track. If the car speeds up at a steady 1.3 m/s^2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

c = 300 m
a_t = 1.3 m/s^2

2. Relevant formulas

a_c = v^2 / r -- Centripetal Acceleration
t = (v_f - v_i) / a -- Time
r = c / 2π -- Radius

The Attempt at a Solution

[/B]
r = 300 / 2π = 150 / π

The diameter of the track was given as 300 m. What is the radius then?

a_t = a_c = 1.3 = v^2 / (150 / π)
v = sqrt((150 / π) * (1.3))
t = (sqrt((150 / π) * (1.3)) - 0) / 1.3 = 6.06 seconds

This isn't correct though... It would appear the answer should be ~11 seconds. Help? Lol.

 

[cnh1995]

A new car is tested on a 300-m-diameter track.

r = 300 / 2π = 150 / π

You are confusing diameter with circumference.

 

[klm_spitfire]

The diameter of the track was given as 300 m. What is the radius then?

G'wah! 150 m. I must've glossed over the "diameter" in "300-m-diameter track" a dozen times. Late night homework sessions don't do me good. Thanks!