Question

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure. The length of the arc ABC is 240 m, and the car completes the turn in 39.0 s.find the magnitude.

Answer 1

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure. The length of the arc ABC is $240\mathrm{m}$, and the car completes the turn in $39.0\mathrm{s}$. Find the magnitude of the acceleration when the car is at point B.

Solution

The length of the arc is for a 90 degree or $\left(\frac{\pi}{2}\right)$ radians is $l = r\theta = 240\mathrm{m} * \left(\frac{\pi}{2}\right) = 377\mathrm{m}$.

So the constant speed is $= \frac{l}{t} = \frac{377}{39} = 9.67\frac{\mathrm{m}}{\mathrm{s}}$.

An acceleration at a uniform speed on a circular curve is $a = \frac{v^2}{r} = \frac{9.67^2}{240} = 0.39\frac{\mathrm{m}}{\mathrm{s}^2}$.

Answer: $0.39\frac{\mathrm{m}}{\mathrm{s}^2}$.