Answer:
The truck will skid for 151 ft before stopping when the brakes are applied
Step-by-step explanation:
From the equations of motion, we will use
![v^{2} = u^{2}-2aS](https://tex.z-dn.net/?f=v%5E%7B2%7D%20%3D%20u%5E%7B2%7D-2aS)
<em>We have to make sure that the parameters we are working with are in the same unit of length. Here, we will be converting from ft to miles</em>
<em>When the truck is travelling at 10 mph.</em>
S = distance the truck skids = ![\frac{5ft}{5286ft/mile}= 0.00094697miles](https://tex.z-dn.net/?f=%5Cfrac%7B5ft%7D%7B5286ft%2Fmile%7D%3D%200.00094697miles)
Final velocity of truck, v = 0 m/s <em>(this is because the truck decelerates to a halt)</em>
Initial velocity of truck u = 10 mph
Hence, we have
![0^{2}=10^{2}-2a\times 0.00094697](https://tex.z-dn.net/?f=0%5E%7B2%7D%3D10%5E%7B2%7D-2a%5Ctimes%200.00094697)
![a= 52799.9miles/hr^{2}](https://tex.z-dn.net/?f=a%3D%2052799.9miles%2Fhr%5E%7B2%7D)
This is the deceleration of the truck
<em>We will work based on the assumption that the car decelerates at the same rate each time the brakes are fully applied.</em>
<em />
<em>When the truck is travelling at u= 55 mph.</em>
We will need to use the deceleration of the car to find the distance traveled when it skids.
![0^{2}=55^{2}-2\times52799.98\times S](https://tex.z-dn.net/?f=0%5E%7B2%7D%3D55%5E%7B2%7D-2%5Ctimes52799.98%5Ctimes%20S)
![S= 0.0286 miles\approx 151 ft](https://tex.z-dn.net/?f=S%3D%200.0286%20miles%5Capprox%20151%20ft)
∴The car skids for about 151 ft when it is travelling at 55 mph and the brakes are applied.