car leaves skid mark 72m in length with a deceleration speed of 7.20m/s^2. what was the initial speed prior to braking?
See previous post: Fri, 1-23-15, 5:42 PM.
To find the initial speed of the car prior to braking, we can use the kinematic equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d).
The equation is:
vf^2 = vi^2 + 2ad
In this case, the final velocity (vf) is 0 m/s because the car comes to a stop. The acceleration (a) is given as -7.20 m/s^2 (negative because it's deceleration). The displacement (d) is the length of the skid mark, which is 72 m.
Now, we can substitute the given values into the equation:
0^2 = vi^2 + 2(-7.20) * 72
Simplifying,
0 = vi^2 - 1036.8
Rearranging the equation to solve for vi:
vi^2 = 1036.8
Taking the square root of both sides:
vi = √1036.8
Calculating,
vi ≈ 32.18 m/s
Therefore, the initial speed of the car prior to braking was approximately 32.18 m/s.