You're driving down the highway at 20m/s when you see a dog you don't want to crush it 35 m in front of you. Your reaction time before stepping on the brakes is 0.5s, and acceleration created by your brakes is 10 m/s^2 what was the distance travelled before coming to a stop?

Question

You're driving down the highway at 20m/s when you see a dog you don't want to crush it 35 m in front of you. Your reaction time before stepping on the brakes is 0.5s, and acceleration created by your brakes is 10 m/s^2 what was the distance travelled before coming to a stop?

Answer 1

before you hit the brakes you go:

20*.5 = 10 meters

then
Vi = 20 m/s
a = - 10 m/s^2
v = Vi + a t
v = Vi - 10 T
0 = 20 - 10 t
t = 2 seconds to stop after hitting brakes
x = Xi + Vi t + .5 a t^2
d = 10 + 20 t - 5 t^2
d = 10 + 40 - 20
d = 30 meters
we stopped 5 meters before the dog

Answer 2

I feel bad for you. school sucks

Answer 3

To find the distance traveled before coming to a stop, we will need to consider two parts: the distance traveled during the reaction time and the distance traveled while braking.

1. Distance traveled during the reaction time:
During the reaction time of 0.5 seconds, the car continues to move at a constant speed. The formula to calculate the distance during this time is given by:
Distance = Speed x Time

Given:
Speed = 20 m/s (constant speed during reaction time)
Time = 0.5 seconds

Distance = 20 m/s x 0.5 s = 10 meters

Therefore, the car traveled 10 meters during the reaction time.

2. Distance traveled while braking:
To determine the distance traveled while braking, we need to use the equation of motion:
Distance = Initial velocity x Time + 0.5 x Acceleration x Time^2

Given:
Initial velocity = 20 m/s
Acceleration = -10 m/s^2 (negative as it acts in the opposite direction to the car's motion)
Time = to be determined

We need to find the time it takes for the car to come to a complete stop. We can use the following kinematic equation:
Final velocity^2 = Initial velocity^2 + 2 x Acceleration x Distance

Final velocity = 0 m/s (since the car comes to a stop)
Initial velocity = 20 m/s
Acceleration = -10 m/s^2

0^2 = 20^2 + 2 x (-10) x Distance
0 = 400 - 20 x Distance
20 x Distance = 400
Distance = 400 / 20
Distance = 20 meters

So, the distance traveled while braking is 20 meters.

Now, to find the total distance traveled before coming to a stop, we can add the distance during reaction time and the distance while braking:
Total Distance = Distance during reaction time + Distance while braking
Total Distance = 10 meters + 20 meters
Total Distance = 30 meters

Therefore, the car traveled a distance of 30 meters before coming to a stop.