Answer:
19.4 seconds
Explanation:
We have:
m: mass of the car = 1500 kg
v₀: is the initial speed = 19 m/s
[tex]v_{f}[/tex]: is the final speed = 0 (it stops)
[tex]\mu_{k}[/tex]: is the coefficient of kinetic friction = 0.100
First, we need to find the acceleration by using the second Newton's law:
[tex] \Epsilon F = ma [/tex]
[tex] -\mu_{k}N = ma [/tex]
[tex] -\mu_{k}mg = ma [/tex]
Solving for a:
[tex] a = -\mu_{k}g = -0.1*9.81 m/s^{2} = -0.981 m/s^{2} [/tex]
Now we can find the time until it stops:
[tex] v_{f} = v_{0} + at [/tex]
Solving for t:
[tex] t = \frac{v_{f} - v_{0}}{a} = \frac{-(19 m/s)}{-0.981 m/s^{2})} = 19.4 s [/tex]
Therefore, the time until it stops is 19.4 seconds.
I hope it helps you!
