Answer
(a) The speed of the car is $17.7~m/s$
(b) The radial acceleration component of the car is $6.27~m/s^2$
(c) The magnitude of the total acceleration is $6.58~m/s^2$
Work Step by Step
(a) We can find the distance of $\frac{1}{4}$ of the circumference:
$d = \frac{1}{4}\times 2\pi~r = \frac{1}{4}(2\pi)(50.0~m) = 78.54~m$
We can find the speed of the car after covering this distance:
$v_f^2 = v_0^2+2ad$
$v_f = \sqrt{v_0^2+2ad}$
$v_f = \sqrt{0+(2)(2.00~m/s^2)(78.54~m)}$
$v_f = 17.7~m/s$
The speed of the car is $17.7~m/s$
(b) We can find the radial acceleration component of the car:
$a_c = \frac{v^2}{r}$
$a_c = \frac{(17.7~m/s)^2}{50.0~m}$
$a_c = 6.27~m/s^2$
The radial acceleration component of the car is $6.27~m/s^2$
(c) We can find the magnitude of the total acceleration:
$a = \sqrt{(2.00~m/s^2)^2+(6.27~m/s^2)^2} = 6.58~m/s^2$
The magnitude of the total acceleration is $6.58~m/s^2$
