To find the distance required for the car to stop, we need to calculate the deceleration of the car using the given information and then use the kinematic equation relating distance, initial velocity, final velocity, and acceleration.
1. Calculate the deceleration:
The deceleration of the car can be determined using the coefficient of friction between the tires and the road. The formula for deceleration is:
deceleration = coefficient of friction * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
So, deceleration = 0.70 * 9.8 m/s^2 = 6.86 m/s^2
2. Use the kinematic equation:
The kinematic equation relating distance (d), initial velocity (u), final velocity (v), and acceleration (a) is:
v^2 = u^2 + 2ad
In this case, the initial velocity (u) is 20 m/s, the final velocity (v) is 0 m/s (as the car stops), and the acceleration (a) is -6.86 m/s^2 (negative because it's decelerating).
Plugging in the values, the equation becomes:
0^2 = 20^2 + 2 * (-6.86) * d
3. Solve for distance (d):
0 = 400 - 13.72d
Move -400 to the other side:
13.72d = 400
Divide both sides by 13.72:
d = 400 / 13.72 ≈ 29.16 meters
Therefore, the car required approximately 29.16 meters to come to a stop.