Answer :
Answer:
-1000N
Explanation:
Given:
[tex]v_{i} = 67 mph \\v_{f} = 49 mph\\d = 200m \\1 mi = 1609 m \\m = 1000kg[/tex]
Solve for:
[tex]Force[/tex]
Principle to Use: Work - Energy Principle
First, we need to convert the velocities from miles per hour to meters per second.
[tex]1 mph = \frac{1609m}{3600s} = 0.44694 m/s \\[/tex]
67 × 0.44694 = 29.94498 m/s
49 x 0.44694 = 21.90006 m/s
Then, we can calculate the initial and final kinetic energies to solve for work.
Kinetic Energy Formula: [tex]\frac{1}{2}mv^2[/tex]
Final Kinetic Energy:
[tex]KE_{f} = \frac{1}{2}(1000)(21.90006^2)\\KE_{f} = 239806.314 J[/tex]
Initial Kinetic Energy:
[tex]KE_{i} = \frac{1}{2}(1000)(29.94498^2)\\KE_{I} = 448350.9136J[/tex]
Work is equal to the change in the kinetic energy.
Work = Final - Initial
239806.314 J - 448350.9136 J = 208544.5996
Work = F times distance
F = Work/distance
F = -208544.5996J/200m
F = -1042.722998 N
Round to nearest thousand
-1042.722998N ---> -1000N
