A car skids to a stop. The length of the skid marks is 50m. What information do you need in order to decide whether the car was speeding before the driver hit the brakes
v = Vi - a t if constant deacceleration a
at stop v = 0
so
a t = Vi , the initial speed
now
d = skid length = average speed during stop * t
so 50 meters = Vi/2 * t
or
Vi *t = 100
now we need some physics
F = m a
so
m a = mu * m g = stopping force
where mu is the coefficient of friction between tires and road
so
a = mu * g
put that back in
a t = Vi = mu * g * t
but we know t = 100/Vi
so
Vi = mu * g * 100 / Vi
Vi^2 = 100 * mu * g
so all we need is that coefficient of friction and g which is about 9.81 m/s^2 on earth
Thanks so much!
You are welcome.
V^2 = Vo^2 + 2a*d;
0 = Vo^2 + 2a*50.
So, to find the initial velocity(Vo); I'll need to know the deacceleration.
To determine whether the car was speeding before the driver hit the brakes, you would need additional information related to the car and its motion. Specifically, you would need at least one of the following pieces of information:
1. Time taken to skid: If you know the time it took for the car to come to a stop after the brakes were applied, you can calculate the car's initial velocity using the formula: initial velocity (u) = (final velocity (v) * t) + (1/2 * acceleration * t^2), where t is the time taken to skid, and assuming the car's acceleration is constant.
2. Coefficient of friction: If you know the coefficient of friction between the car's tires and the road surface, you can calculate the car's initial velocity by using the equation: initial velocity (u) = sqrt(2 * acceleration * friction coefficient * skid distance), where skid distance is the length of the skid marks.
3. The condition of the road surface: If you have information about the road surface conditions, such as whether it was dry, wet, icy, or any other relevant factor, you can analyze the impact it would have had on the car's skid distance. Different road conditions may affect the skid marks differently, which can help in determining the car's initial speed.
It's important to note that the determination of whether the car was speeding also depends on the legal speed limit in the area. If the car's initial velocity is higher than the speed limit, it can be inferred that the car was speeding before hitting the brakes.