Question

Taryn was driving down the road at 90 km/hr when he sees a deer running into the road in front of him. He applies the brakes and decelerates at 3.7 m/s². How much distance does Taryn need to stop in order to save the deer's life?

Answer 1

To calculate the distance that Taryn needs to stop in order to save the deer's life, we can use the equation v^2 = u^2 + 2as, where v is the final velocity (0 m/s), u is the initial velocity (25 m/s), a is the acceleration (-3.7 m/s²), and s is the distance we want to find. By plugging in the values and solving the equation, we find that Taryn needs to stop in approximately 84.459 meters.

Step-by-step explanation:

To calculate the distance that Taryn needs to stop in order to save the deer's life, we need to determine the time it takes for Taryn to come to a stop after applying the brakes. We can use the equation:

v^2 = u^2 + 2as

where v is the final velocity (0 m/s, since Taryn comes to a stop), u is the initial velocity (90 km/hr, which we need to convert to m/s), a is the acceleration (-3.7 m/s²), and s is the distance we want to find.

First, let's convert Taryn's initial velocity from km/hr to m/s:

90 km/hr * (1000 m/1 km) * (1 hr/3600 s) = 25 m/s

Now we can plug the values into the equation:

(0 m/s)^2 = (25 m/s)^2 + 2(-3.7 m/s²)s

Simplifying the equation, we get:

0 = 625 + 2(-3.7)s

Solving for s, we find:

s = -625 / (-2 * 3.7)

s ≈ 84.459 m

Therefore, Taryn needs to stop in approximately 84.459 meters to save the deer's life.