A car moves around a curved path that has a radius of 375 feet. While moving aro

Question

A car moves around a curved path that has a radius of 375 feet. While moving around the arced path, the car increases speed by 1.15 ft/s^2.
If the car starts from rest, determine the time needed to reach an acceleration of 5.5 ft/s^2.
Determine the speed of the car at the instant the acceleration is 7.25 ft/s^2.
Determine the magnitude of the acceleration at the instant the speed of the car is 28 ft/s.
Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.25 ft/s^2.

Explanation / Answer

r = 375
at=1.15 ft/s^2

A)

a2 = ar2+at2

5.52=1.152+ar2

ar=(5.52-1.152)=5.38

ar=v2/r

(5.38 x 375) = v

v=44.92 ft/s

v=u+at

44.92 = 1.15t

t=39.06 s

B)

a2 = ar2+at2

7.252=1.152+ar2

ar=(7.252-1.152)=7.158

ar=v2/r

(7.158 x 375) = v

v=51.81 ft/s

C)

ar=v2/r = 28^2/375 = 2.091

a2 = ar2+at2

a=(2.0912+1.152)=2.3864

D)

when maximum acceleration = 7.25

a=v^2/r

(7.25 x 375)= v

v=52.142 ft/s

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