Question

It is friction that provides the force for a car to accelerate, so for high-performance cars the factor that limits acceleration isn't the engine; it's the tires. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. Part A For typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 70 mph? Suppose that μs=1.00 and μk=0.80.

Answer 1

The time which a car could accelerate from 0 to 70mph with a us=1.00 and uk=0.80 is

`t=3.99s`

Step-by-step explanation:

The net force knowing the accelerations must be determinate to get the speed goal

∑F=Fs-Fk=m*a

`F_(s)=u_(s)*F_(N)=u_(s)*m*g`

`F_(k)=u_(k)*F_(N)=u_(k)*m*g`

`u_(s)*m*g-u_(k)*m*g=m*a`

`a=(u_(s)-u_(k))*g`

`a=0.80*9.8m/s^2`

`a=7.84 m/s^2`

So knowing the acceleration and knowing the speed the car must get using equation of uniform motion accelerated

`v_(f)=v_(i)+a*t`

`70mph*(1.60934km)/(1mi)*(1000m)/(1km)*(1h)/(3600s)=31.29 (m)/(s)`

`31.29 m/s=1.96m/s^2*t`

`t=(31.29m/s)/(7.84m/s^2)`

`t=3.99s`