An automobile whose speed is increasing at a rate of 0.400 m/s2 travels along a

Question

An automobile whose speed is increasing at a rate of 0.400 m/s2 travels along a circular road of radius 10.0 m. (a) When the instantaneous speed of the automobile is 5.00 m/s, find the tangential acceleration component. Magnitude Direction O in a direction opposite to the automobile's motion O in the direction of the automobile's motion (b) What is the centripetal acceleration component? Magnitude Direction O away from the center of curvature O toward the center of curvature (c) Determine the magnitude and direction of the total acceleration. Magnitude Direction o outward from the automobile's path inward from the automobile's path

Explanation / Answer

a)

at = tangential acceleration = 0.4 m/s2

in the direction of automobile's motion

b)

centripetal acceleration is given as

ac = v2/r = 52/10 = 2.5 m/s2

direction: towards the center of curvature

c)

a = total acceleration = sqrt(ac2 + at2) = sqrt((0.4)2 + (2.5)2) = 2.53 m/s2

inward from automobile's path

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