Tracy K. answered • 11/14/17

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- F = ma
- We must first calculate a, the acceleration, before applying the F= ma equation to determine the force.
- In order to calculate the acceleration, we must first use the following equation of kinematics, Vf
^{2}= Vi^{2}+ 2ax. - V
_{f}= final velocity = 0 meters/second. (The vehicle is stopped) - V
_{i}= initial velocity = 89 kilometers/hour, however, this must be converted to meters/second = 24.72 m/s - a = acceleration = quantity that we are attempting to calculate
- x = distance = 110 meters
**rearranging the formula, a = (V**_{f}^{2}- V_{i}^{2})/2X = (0 - 611.2)/2(110) ≅ 2.78 m/s^{2}(In Magnitude)_{}**F = ma = (1070 Kg)(2.78 m/s**^{2}) ≅ 2972 Kg·m/s^{2}or 2972 Newtons ( 1 Newton = 1 Kg·m/s^{2})**For the second part, just replace X=110 to X=2.34****a = (Vf**^{2}- Vi^{2})/2X = (0 - 611.2)/2(2.34) ≅ 130.6 m/s^{2}**F = ma = (1070 Kg)(130.6 m/s**^{2}) ≅ 139,740 Newtons**This force is about 47 times greater than the force in the initial portion****The same mass is brought to a halt from the same speed; however, this occurs over a much shorter distance and time interval in the second part. Notice that the Force ratio is equal to the ratio of Accelerations**