Concept explainers
When the speed of the race car in Example 5–16 is 30 m/s, how are (a) atan and (b) aR changed?
EXAMPLE 5–16 Two components of acceleration. A race car starts from rest in the pit area and accelerates at a uniform rate to a speed of 35 m/s in 11 s, moving on a circular track of radius 500 m. Assuming constant tangential acceleration, find (a) the tangential acceleration, and (b) the radial acceleration, at the instant when the speed is v = 15 m/s.
APPROACH The tangential acceleration relates to the change in speed of the car, and can be calculated as atan = Δv/Δt. The centripetal acceleration relates to the change in the direction of the velocity vector and is calculated using aR = v2/r.
SOLUTION (a) During the 11-s time interval, we assume the tangential acceleration atan is constant. Its magnitude is
(b) When
NOTE The radial acceleration increases continually, whereas the tangential acceleration stays constant.
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