Question

When the driver applies the brakes of a small-size truck traveling 10 mph, it skids 5 ft before stopping. How far will the truck skid if it is traveling 55 mph when the brakes are applied

Answer 1

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

$v^{2} = u^{2}-2aS$

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

When the truck is travelling at 10 mph.

S = distance the truck skids = $\frac{5ft}{5286ft/mile}= 0.00094697miles$

Final velocity of truck, v = 0 m/s (this is because the truck decelerates to a halt)

Initial velocity of truck u = 10 mph

Hence, we have

$0^{2}=10^{2}-2a\times 0.00094697$

$a= 52799.9miles/hr^{2}$

This is the deceleration of the truck

We will work based on the assumption that the car decelerates at the same rate each time the brakes are fully applied.

When the truck is travelling at u= 55 mph.

We will need to use the deceleration of the car to find the distance traveled when it skids.

$0^{2}=55^{2}-2\times52799.98\times S$

$S= 0.0286 miles\approx 151 ft$

∴The car skids for about 151 ft when it is travelling at 55 mph and the brakes are applied.