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.
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.