Question

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

Answer 1

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

Step-by-step 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 = (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

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

Initial velocity,
`u` = 20 m/s

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

Let the distance traveled here be
`s`

From one of the equations of kinematics for linear motion

`v^(2) = u^(2) + 2as`

Where,
`v` is the final velocity

`u` is the initial velocity

`a` is acceleration

and
`s` 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 = (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