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

Answer:

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

$t=3.99s$

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

$v_{f}=v_{i}+a*t$

$70mph*\frac{1.60934km}{1mi}*\frac{1000m}{1km}*\frac{1h}{3600s}=31.29 \frac{m}{s}$

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

$t=\frac{31.29m/s}{7.84m/s^2}$

$t=3.99s$