A race car accelerates uniformly from a speed of 39.5 m/s to a speed of 56.0 m/s

Question

A race car accelerates uniformly from a speed of 39.5 m/s to a speed of 56.0 m/s in 5.00 s while traveling clockwise around a circular track of radius 4.10 x 10^2 m. When the car reaches a speed of 50.0 m/s, find the following.
(a) the magnitude of the centripetal acceleration
m/s2

(b) the angular speed
rad/s

(c) the magnitude of the tangential acceleration
m/s2

(d) the magnitude of the total acceleration
m/s2


Suppose the race car now slows down uniformly from 56.0 m/s to 23.0 m/s in 3.50 s to avoid an accident, while still traveling a circular path 4.10 x 10^2 m in radius.
(a) Find the magnitude of the centripetal acceleration when the speed is 40.0 m/s.
m/s2

(b) Find the angular speed when the speed is 40.0 m/s.
rad/s

(c) Find the magnitude of the tangential acceleration when the speed is 40.0 m/s.
m/s2

(d) Find the magnitude of the total acceleration when the speed is 40.0 m/s.
m/s2

Explanation / Answer

a) Ac =v^2 /R =50^2 /410 =6.1m/s^2 .

b ) =V/R =50/410 =0.122rad/s

c)At =(v2-v1)/(t) =(56 -39.5)/5 =3.3 m/s^2 .

d)) A =[(Ac^2 +At^2 )]^.5 =[(6.1^2)+(3.3^2)]^.5 = 6.94m/s .

2

a )Ac =v^2 /R =(40^2 )/410 = 3.90 m/s^2 .

b) =V/R = 40/410 =0.1rad/s .

c) At =(v2-v1)/(t) =(23-56)/3.5 =-9.43

modulus of At = 9.43 m/s^2 .

d) A =[(Ac^2 +At^2 )]^.5 =[104.1349]^.5 = 10.2 m/s^2 .

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