Given:
Mass of car, m = 2000 kg
Coefficient of kinetic friction, μk = 0.70
Distance = 75 m
Let's find the speed of the car.
To find the speed of the car, apply the motion formula:
[tex]v^2=u^2+2as[/tex]Where:
v is the final velocity = 0 m/s
u is the initial velocity
a is the acceleration of the car.
s is the distance = 75 m
To find the acceleration, we have:
[tex]a=-\mu_k*g[/tex]Where:
μk = 0.70
g is acceleration due to gravity = 9.8 m/s²
Thus, we have:
[tex]\begin{gathered} a=-0.70*9.8 \\ \\ a=-6.86\text{ m/s}^2 \end{gathered}[/tex]The deceleration of the car is -6.86 m/s².
Now, to find the initial velocity u, we have:
[tex]\begin{gathered} v^2=u^2+2as \\ \\ 0^2=u^2+2(-6.86)(75) \\ \\ 0=u^2-1029 \\ \\ u^2=1029 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{u^2}=\sqrt{1029} \\ \\ u=32.08\text{ m/s} \end{gathered}[/tex]Therefore, the speed of the car was 32.08 m/s.
ANSWER:
32.08 m/s
