You are driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s , and the maximum deceleration of your car is 10 m/s2 . How much distance is between you and the deer when you come to a stop?
Answer=5m
You found the distance that you will cover while braking. You can use the expected amount of time for braking to check your answer for distance.
Using the information given in the introduction and the value for distance that you found above, determine the time required for you to stop once you press the brakes. Note that the time for braking is just the time interval t3−t2.
----Not quite sure what to do
Just 2
1. calculate distance travelled before brakes have effect.
2. Once deceleration of 10 m/s² starts, car decelerates at that rate.
Time taken to decelerate = initial velocity / 10 m/s² = 2 seconds.
3. Calculate distance travelled during those two seconds:
vf²=vi²+2*a*Δx
vf=final speed = 0
vi = initial speed = 20 m/s
a=acceleration = -10 m/s²
Solve for Δx (distance travelled) and add to the "thinking" time found in step 1.
Well, let's go step by step and figure it out together!
First, let's calculate the distance you will cover during your reaction time. Since you're traveling at a constant speed of 20 m/s, the distance covered during your reaction time is simply:
Distance during reaction time = speed × time = 20 m/s × 0.50 s = 10 m
So, initially, there is a distance of 10 meters between you and the deer.
Next, let's determine how much distance you will cover while braking. To do that, we need to find the distance required to bring your car to a stop. We can use the following equation of motion:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity (0 m/s, since the car comes to a stop)
vi = initial velocity (20 m/s)
a = acceleration (deceleration in this case, -10 m/s^2)
d = distance
Rearranging the equation, we get:
d = (vf^2 - vi^2) / (2a)
Plugging in the values:
d = (0^2 - 20^2) / (2 × -10)
Simplifying further:
d = 400 / -20
d = -20 m
Uh-oh, it seems we got a negative value for distance, which doesn't make sense. That means we made a mistake somewhere!
Let's go back and double-check our calculations.
To solve this problem, we can break it down into different time intervals and calculate the distance covered during each interval.
First, let's calculate the distance covered during the reaction time. The reaction time is given as 0.50 s. Since you are traveling at a constant speed of 20 m/s, the distance covered during this time interval can be calculated using the formula: distance = speed × time.
Distance covered during reaction time = 20 m/s × 0.50 s = 10 m.
Next, let's calculate the distance covered during the braking period. We need to determine the time it takes for the car to come to a stop. This can be calculated using the formula: time = change in velocity / acceleration.
Change in velocity = final velocity - initial velocity = 0 m/s - 20 m/s = -20 m/s (negative because the car is decelerating).
Acceleration = -10 m/s² (negative because it is the braking deceleration).
Time taken to stop = change in velocity / acceleration = (-20 m/s) / (-10 m/s²) = 2 s.
Now, we can calculate the distance covered during the braking period using the formula: distance = speed × time.
Distance covered during braking = 20 m/s × 2 s = 40 m.
Finally, we can find the total distance between you and the deer when you come to a stop by adding the distances covered during the reaction time and the braking period.
Total distance = distance covered during reaction time + distance covered during braking = 10 m + 40 m = 50 m.
Therefore, when you come to a stop, there will be a distance of 50 meters between you and the deer. This is different from the given answer of 5 meters.