Police find skid marks 180 meters long on a highway where a car made an emergency stop. Assuming that the deceleration was a = 10 m/s¶ (about the maximum for dry pavement), how fast was the car traveling before the brakes were applied?
s=(v₀²-v²)/2a
v= sqrt{ v₀²-2as}
klyo
To find the speed of the car before the brakes were applied, we can use the formulas of motion and the concept of deceleration.
Firstly, let's identify the given information:
- Deceleration (a) = -10 m/s^2 (negative since it refers to deceleration)
- Skid marks length (s) = 180 meters
The formula we can use to find the speed is:
v² = u² + 2as
where:
v = final velocity (which is 0 m/s since the car came to a stop)
u = initial velocity (the speed we are trying to find)
a = acceleration (deceleration in this case, which is -10 m/s^2)
s = distance (the length of the skid marks, which is 180 meters)
Substituting the given values into the formula, we have:
0² = u² + 2(-10)(180)
Simplifying:
0 = u² - 3600
Rearranging the equation to isolate u²:
u² = 3600
Taking the square root of both sides:
u = √3600
Calculating:
u ≈ 60 m/s
Therefore, the car was traveling at approximately 60 meters per second (m/s) before the brakes were applied.