Ann is driving down a street at 58 km/h. Suddenly a child runs into the street. If it takes Ann .71 s to react and apply the brakes, how far will she have moved before she begins to slow down? Answer in units of m.
When I converted 58km/h I got 16.111 m/s but now I'm not really sure how to solve problem.
You are on the right track. Your conversion to m/s looks good.
The question is how far does the car move in 0.71s.
distance = rate*time
= 16.111m/s * 0.71s
=11.44m
To solve this problem, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, we know the initial velocity (58 km/h) and the time it takes for Ann to react and apply the brakes (.71 s). However, we don't know the acceleration.
We can start by converting the initial velocity from km/h to m/s:
58 km/h * (1000 m/km) / (3600 s/h) = 16.11 m/s
Next, we need to find the acceleration. The acceleration can be calculated using the formula:
acceleration = change in velocity / time
In this case, we want to find the change in velocity. The change in velocity can be calculated using the equation:
change in velocity = final velocity - initial velocity
Since the child suddenly runs onto the street, Ann needs to slow down to avoid hitting the child. Assuming she stops completely (final velocity = 0 m/s), we can calculate the change in velocity:
change in velocity = 0 - 16.11 m/s = -16.11 m/s
Now we can calculate the acceleration:
acceleration = change in velocity / time
acceleration = (-16.11 m/s) / (.71 s) ≈ -22.71 m/s^2
Finally, we can plug the values into the formula to find the distance:
distance = initial velocity * time + (1/2) * acceleration * time^2
distance = (16.11 m/s) * (.71 s) + (1/2) * (-22.71 m/s^2) * (.71 s)^2
distance ≈ 5.74 m + (1/2) * (-22.71 m/s^2) * (.5041 s^2)
distance ≈ 5.74 m + (1/2) * (-11.44 m) = 5.74 m - 5.72 m ≈ 0.02 m
Therefore, Ann will have moved approximately 0.02 meters before she begins to slow down.
To solve this problem, you can break it down into two parts: the distance Ann travels during her reaction time, and the distance she travels while decelerating to rest.
First, let's calculate the distance traveled during Ann's reaction time:
Given that Ann's reaction time is 0.71 s, we can use the formula:
Distance = Speed × Time
Distance = 16.111 m/s × 0.71 s
So, Ann would have traveled a distance of approximately 11.437 m during her reaction time.
Next, let's calculate the distance Ann travels while decelerating to rest:
Since Ann needs to come to a stop, we can assume she applies the brakes until her speed reaches zero. To calculate the distance she travels while decelerating, we need to use the formula for the distance traveled during uniform acceleration:
Distance = (Initial Speed × Time) + (0.5 × Acceleration × Time^2)
Since Ann is slowing down, her initial speed is 16.111 m/s and her final speed is 0 m/s.
Since we are not given the deceleration or time taken to come to rest, we have insufficient information to directly calculate the distance traveled while decelerating.
Therefore, the total distance Ann will have moved before she begins to slow down would be the sum of the distance traveled during her reaction time (11.437 m) and the distance traveled while decelerating (which we cannot determine without more information).