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

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

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

Where, is the final velocity

is the initial velocity

is acceleration

and is the distance traveled

Putting the values into the equation, we get

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

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