Answer:
(a) 0.158 rad/s.
(b) 7.1 m/s² toward the center of the circular track.
Explanation:
(a)
Using,
v = ωr.................. Equation 1
Where v = speed of the car, r = radius of the circular track. ω = angular speed.
make ω the subject of the equation
ω = v/r ................... Equation 2
Given: v = 45 m/s, r = 285 m.
substitute into equation 2
ω = 45/285
ω = 0.158 rad/s
Hence the magnitude of the angular speed of the car = 0.158 rad/s.
(b)
Using
a = v²/r......................... Equation 3
Where a = acceleration of the car
Given: v = 45 m/s, r = 285 m
Substitute into equation 3
a = 45²/285
a = 2025/285
a = 7.1 m/s² toward the center of the circular track.