At time t = 0 s, automobile A is traveling at a speed of 17.1 m/s along a straig

Question

At time t = 0 s, automobile A is traveling at a speed of 17.1 m/s along a straight road and is picking up speed with an acceleration that has a magnitude of 3.50 m/s2 as in part a of the figure. At t = 0 s, automobile B is traveling at a speed of 17.1 m/s in uniform circular motion as it negotiates a turn (part b of the figure). It has a centripetal acceleration whose magnitude is also 3.50 m/s2. Determine the speed of (a) automobile A and (b) automobile B, when t = 2.0 s.

Explanation / Answer

Given that

Automobile A is traveling at a speed of (Vo) =17.1 m/s along a straight road

The magnitude of acceleration (ac) =3.50 m/s2

a)

The speed of the automobile A at a time t =2s is

vA =vo+at = (17.1m/s)+(3.50 m/s2)(2s) =24.1m/s

b)

Now the speed of the automobile B in a time t =2s is

ac =v2/R then the radius becomes R =v2/ac =(17.1m/s)2/3.50m/s2 =83.545m

The vB =w*R =(2pi/T)*R =(2pi/2)*(83.545m) =262.333m/s

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