Posted by **senko** on Monday, October 8, 2012 at 1:26pm.

A car starts from rest on a curve with a radius of 110m and accelerates at 1.2m/s^2. Through what angle will the car have traveled when the magnitude of its total acceleration is 2.1 m/s^2?

I thought i got the answer which was 0.75 rad or 43 degrees but it says its the wrong answer or the rounding is wrong. Please help!!!

Steps please.

- Physics Circular motion -
**Elena**, Monday, October 8, 2012 at 2:34pm
tangential acceleration is a(τ)= 1.2 m/s²

normal acceleration is a(n) = ω²R,

whwre ω is the angular velocity.

a=2.2 m/s²

a² = a(τ)²+ a(n)² = a(τ)²+ (ω²•R)²

ω⁴ = { a²-a(τ)²)/R² =(2.1²-1.2²)/110² = 2.45•10⁻⁴

ω=0.125 rad/s

The angular acceleration is

ε= a(τ)/R = 1.2/110 = 0.011 rad/s²

ω=ε•t => t=ω/ε

φ = ε•t²/2 = ε•ω²/2•ε²=ω²/2•ε =

=0.125²/2•0.011 = 0.71 rad.

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