A detective is investigating a scene of an accident. He measures the length of an automobile's skid marks to find out how fast the automobile was going at the very beginning of the skid. Express In terms of V ( speed), L ( length) and any other suitable variables related to this problem
initial speed = V
final speed = 0
length of skid = L
assume constant road/tire friction coefficient = mu
a = magnitude of deacceleration
0 = V - a t
so
t = V/a time to stop
L = V t - (1/2) a t^2
L = V(V/a) - (1/2)a(V^2/a^2)
so
L = (1/2)(V^2/a)
a = V^2/2L
now physics
F = m a = mu m g
mu m g = m V^2/L
L mu g = V^2
so
V = sqrt(mu g) sqrt L
g = 9.81 m/s^2
I bet the detective knows mu for tire and road
So he can estimate speed V from skid length L
breaking force = F = -
why is it
mu m g =m V^2/L instead of mu m g= m V^2/2L?
sorry, missed the 2
I checked the units but not the constants
To express the speed of the automobile at the beginning of the skid in terms of the length of the skid marks (L) and any other suitable variables, we can use the formula for calculating speed using skid marks.
The formula is:
Speed (V) = (2 * L * g) / f
Here, g represents the acceleration due to gravity, and f represents the coefficient of friction between the tires and the road surface.
In order to use this formula, the detective will need to gather additional information. The values for g and f can vary depending on the circumstances of the accident and the road conditions.
The detective can obtain the values for g and f from sources such as accident reports, tire manufacturer data, or consult with experts in accident reconstruction. Once these values are known, the detective can substitute them into the formula along with the length of the skid marks (L) to calculate the initial speed (V) of the automobile.