Respuesta :
Answer:
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
[tex]Velocity = \frac{Distance}{Time}[/tex]
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
[tex]a=[/tex] - 10 m/s² ( Since the car will decelerate after stepping on the brakes)
Initial velocity, [tex]u[/tex] = 20 m/s
Final velocity, [tex]v[/tex] = 0 m/s (Since the car will come to a stop after stepping on the brakes)
Let the distance traveled here be [tex]s[/tex]
From one of the equations of kinematics for linear motion
[tex]v^{2} = u^{2} + 2as[/tex]
Where, [tex]v[/tex] is the final velocity
[tex]u[/tex] is the initial velocity
[tex]a[/tex] is acceleration
and [tex]s[/tex] is the distance traveled
Putting the values into the equation, we get
[tex]0^{2} = 20^{2} + 2 (-10)s[/tex]
[tex]0 = 400 -20s\\[/tex]
[tex]20s = 400[/tex]
[tex]s = \frac{400}{20}[/tex]
[tex]s = 20 m[/tex]
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
