An automobile whose speed is increasing at a rate of 0.400 m/s^2 travels along a

Question

An automobile whose speed is increasing at a rate of 0.400 m/s^2 travels along a circular road of radius 30.0 m. When the instantaneous speed of the automobile is 3.00 m/s, find the tangential acceleration component. in the direction of the automobile's motion in a direction opposite to the automobile's motion What is the centripetal acceleration component? Magnitude Direction away from the center of curvature toward the center of curvature Determine the magnitude and direction of the total acceleration. Magnitude Direction outward from the automobile's path inward from the automobile's path

Explanation / Answer

(A)
Tangential Acceleration, at = 0.4 m/s^2
In the Direction of the Automobile's motion.

(B)
r = 30 m
Centripetal Acceleration, ac = v^2/r
Centripetal Acceleration, ac = 3.0^2/(30)
Centripetal Acceleration, ac = 0.3 m/s^2

Toward the center of Curvature.

(C)
a = sqrt(at^2 + ac^2)
a = sqrt(0.4^2 + 0.3^2)
a = 0.5 m/s^2

Direction = tan^-1(0.3/0.4)
Direction = 36.8o

Inward from the automobile path.

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