Physics, 20.09.2020 14:01 vanesacastorena

You are driving down the highway late one night at 20m/s when a deer steps in onto the road 43m in front of you. You reaction time before stepping on the brakes is 0.50s, and the maximum acceleration of your car is 10m/s^2. How much distance is between you and the deer when you come toa stop

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Answer from: braddypeter61

The distance between you and the deer when you come to a stop is 13m

Explanation:

To determine how much distance is between you and the deer when you come to a stop,

First, we will calculate the distance traveled during the reaction time (that is, before stepping on the break)

The velocity at the time is 20 m/s

and the time (reaction time) is 0.5s

From

$Velocity = \frac{Distance}{Time}$

Then,

Distance = Velocity × Time

Distance = 20 m/s × 0.5 s

Distance = 10 m

This is the distance traveled before stepping on the break.

Now, we will calculate the distance traveled after stepping on the break

The maximum acceleration of the car is 10 m/s²

- 10 m/s² ( Since the car will decelerate after stepping on the brakes)

Initial velocity, = 20 m/s

Final velocity, = 0 m/s (Since the car will come to a stop after stepping on the brakes)

Let the distance traveled here be

From one of the equations of kinematics for linear motion

$v^{2} = u^{2} + 2as$

Where, is the final velocity

is the initial velocity

is acceleration

and is the distance traveled

Putting the values into the equation, we get

$0^{2} = 20^{2} + 2 (-10)s$

$0 = 400 -20s\\$

20s = 400

$s = \frac{400}{20}$

s = 20 m

Hence, the car traveled for another 20m before coming to a stop

The total distance traveled after the deer steps in onto the road is

10m + 20m

= 30m

Since the deer was at a distance 43m away before coming to a stop after traveling a distance of 30m,

Then, the distance between you and the deer is

43m - 30m

= 13m

Hence, the distance between you and the deer when you come to a stop is 13m

Answer from: Quest

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