In coming to a stop, a car leaves skid marks 97.0 m long on the highway. Assuming a deceleration of 6.60 m/s2, estimate the speed of the car just before braking.
(in m/s)
d = (1/2) a t^2
194 = 6.60 t^2
solve for t
then
v = Vi - 6.60 t = 0 at end
Vi = 6.60 t
44ms^1
Sorry it was a typing error
To estimate the speed of the car just before braking, you can use the equation of motion that relates the distance traveled, initial velocity, acceleration, and time:
Distance = (Initial Velocity * Time) + (0.5 * Acceleration * Time^2)
In this case, the distance traveled is given as 97.0 m and the deceleration is given as 6.60 m/s^2.
Considering the car is coming to a stop, we know that the final velocity (Vf) would be 0 m/s. We want to find the initial velocity (Vi).
The equation can be rearranged to solve for Vi:
97.0 m = (Vi * t) + (0.5 * (-6.60 m/s^2) * t^2)
Since we don't know the time (t), it's helpful to solve the equation by substituting another equation that relates Vi, t, and acceleration:
Vi = Vf + (Acceleration * Time)
Since Vf is 0 m/s in this case, the equation becomes:
Vi = Acceleration * Time
Now we can substitute this expression for Vi into the first equation:
97.0 m = ((Acceleration * Time) * t) + (0.5 * (-6.60 m/s^2) * t^2)
Simplifying the equation:
97.0 m = (6.60 m/s^2 * t^2) / 2
Multiply both sides by 2:
194.0 m = 6.60 m/s^2 * t^2
Divide both sides by 6.60 m/s^2:
t^2 = 29.39
Take the square root of both sides to solve for t:
t = √29.39
t ≈ 5.42 seconds
Now, we can substitute the value of t back into the equation for Vi:
Vi = 6.60 m/s^2 * 5.42 s
Vi ≈ 35.712 m/s (rounded to 3 decimal places)
Therefore, the estimated speed of the car just before braking is approximately 35.712 m/s.