A race car accelerates uniformly as it leaves the pit area, going from rest to 2

Question

A race car accelerates uniformly as it leaves the pit area, going from rest to 290 km/h in a semicircular arc (i.e. 1/2 of a circle) with a radius of 190 m.
Determine the tangential acceleration of the car when it is halfway through the turn (i.e. 1/4 of a circle), assuming constant tangential acceleration.
m/s2
Determine the radial acceleration of the car at this time (when it has traveled 1/4 of a circle).
m/s2
If the curve were flat, what would the minimum coefficient of static friction between the tires and the roadbed have to be in order to provide the total acceleration with no slipping or skidding when the car has traveled halfway through the turn?

Explanation / Answer

Radius of the path   =   190 m linear velocity v =   80.55 m/s distance travelled by the object   s =  2 r / 2 =   3.14* 190 m. /2 = 596.6 m Tangential acceleration at = v^2 / 2s    =   5.43 m/s^2 radial accelaration ar    =   v^2 /r   = 34.15   m/s^2 net accelaraion a = sqrt ( (at )^2 + (ar )^2 )   = 34.57 m/s^2 The coeffitient of frictional force   between the tires and road is Since the car not slipped out ma = mv^2 /r solving for =   v^2 /r*a   = .................. net accelaraion a = sqrt ( (at )^2 + (ar )^2 )   = 34.57 m/s^2 The coeffitient of frictional force   between the tires and road is Since the car not slipped out ma = mv^2 /r solving for =   v^2 /r*a   = ..................

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