A car can accelerate forward because its tires push backward against the ground.

Question

A car can accelerate forward because its tires push backward against the ground. If the tires do not slip, the force with which the tires push backward is static friction. The shortest time in which a certain high performance sports car can accelerate from zero to 60 mph is 3.50 seconds. Find the coefficient of static friction between the tires of this car and the ground. (Note: If the driver attempts to accelerate faster, the tires will spin instead. Cars can achieve greater accelerations, but only with special “stickier” tires. Such tires are made of “softer” rubber than normal tires and tend to wear out quickly in normal street driving.)

Explanation / Answer

here,

final speed of car , v = 60 mph

v = 26.82 m/s

time taken by the car , t = 3.5 s

let the accelration be a

using first equation of motion

v = u + a * t

26.82 = 0 + a * 3.5

a = 7.66 m/s

let the coefficient of static friction be u

for the tire not to slip

u*g = a

u*9.8 = 7.66

u = 0.78

the coefficient of static friction between the tires of this car and the ground is 0.78

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