In order to determine the required force to stop the car, proceed as follow:
Calculate the deceleration of the car, by using the following formula:
![v^2=v^2_o-2ax](https://tex.z-dn.net/?f=v%5E2%3Dv%5E2_o-2ax)
where,
v: final speed = 0m/s (the car stops)
vo: initial speed = 36m/s
x: distance traveled = 980m
a: deceleration of the car= ?
Solve the equation above for a, replace the values of the other parameters and simplify:
![\begin{gathered} a=\frac{v^2_o-v^2}{2x} \\ a=\frac{(36\frac{m}{s})^2-(0\frac{m}{s})^2}{2(980m)}=0.66\frac{m}{s^2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D%5Cfrac%7Bv%5E2_o-v%5E2%7D%7B2x%7D%20%5C%5C%20a%3D%5Cfrac%7B%2836%5Cfrac%7Bm%7D%7Bs%7D%29%5E2-%280%5Cfrac%7Bm%7D%7Bs%7D%29%5E2%7D%7B2%28980m%29%7D%3D0.66%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%5Cend%7Bgathered%7D)
Next, consider that the formula for the force is:
![F=ma](https://tex.z-dn.net/?f=F%3Dma)
where,
m: mass of the car = 820 kg
a: deceleration of the car = 0.66m/s^2
Replace the previous values and simplify:
![F=(820kg)(0.66\frac{m}{s^2})=542.20N](https://tex.z-dn.net/?f=F%3D%28820kg%29%280.66%5Cfrac%7Bm%7D%7Bs%5E2%7D%29%3D542.20N)
Hence, the required force to stop the car is 542.20N