In coming to a stop a car leaves skid marks 92m long on the highway. Assuming a decceleration of 7.00m/s^2, estimate the speed of the car just before braking.
d = 0.5 * a * t^2,
92 m = 0.5 * 7.0 m/s^2 t^2,
92 = 3.5t^2,
t^2 = 92/3.5 = 26.29,
t = sqrt(26.29) = 5.13 s.
a = (Vt - Vo) / t,
-7.00 m/s^2 = (0 - Vo) / 5.13 s,
-7.00 = -Vo /5.13,
-Vo = - 7.0 * 5.13 = -35.91,
Vo = 35.91 m/s. = velocity Just before braking.
Where did you get the 0.5?
Well, well, well, looks like we have a "braking" good question here! Let's put on our detective hats and solve this little mystery, shall we?
To estimate the speed of the car just before braking, we can use a little bit of physics. The equation we need to use is:
v^2 = u^2 + 2as
Where:
v is the final velocity (which in this case is 0 m/s, because the car comes to a stop)
u is the initial velocity (the speed we want to find)
a is the acceleration (given as -7.00 m/s^2, because the car is decelerating)
s is the distance (given as 92 m, which is the length of the skid marks)
Rearranging the equation and plugging in the values, we have:
0 = u^2 + 2(-7.00)(92)
Now, let me do some calculations here... *clownish drumroll*
By solving this equation, we find that the speed of the car just before braking was approximately 30 m/s.
So, there you have it! The car was cruising at around 30 meters per second before deciding to slam on the brakes. I hope this answer brought a little humor to your day!
To estimate the speed of the car just before braking, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s because the car comes to a stop)
u = initial velocity (unknown)
a = acceleration (given as -7.00 m/s^2 because the car is decelerating)
s = distance (given as 92 m)
We can rearrange the equation to solve for the initial velocity:
u^2 = v^2 - 2as
Since the car comes to a stop (v = 0), we can simplify the equation to:
u^2 = -2as
Now, substitute the given values into the equation:
u^2 = -2(-7.00 m/s^2)(92 m)
Simplifying further:
u^2 = 1264.00 m^2/s^2
To find the initial velocity (u), we need to take the square root of both sides:
u = √(1264.00 m^2/s^2)
Calculating the square root:
u ≈ 35.5 m/s
Therefore, the estimated speed of the car just before braking is approximately 35.5 m/s.