Suzie (of mass 84 kg) is roller-blading down the sidewalk going 34 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 1.1 seconds.
What is Suzie’s average acceleration? Answer in units of m/s2.
a = change in velocity/ change in time
34 mi/h = 15.2 m/s (use Google)
change in v/time = -15.2/1.1 m/s^2
To find Suzie's average acceleration, we can use the formula:
Average Acceleration = Change in Velocity / Time
First, let's convert Suzie's speed from miles per hour to meters per second (since acceleration is usually measured in m/s^2).
1 mile = 1.60934 kilometers
1 kilometer = 1000 meters
Given that Suzie's speed is 34 miles per hour, we can convert it to meters per second as follows:
34 miles/hour * (1 hour/3600 seconds) * (1.60934 kilometers/mile) * (1000 meters/kilometer) = 15.2056 m/s
Therefore, Suzie's velocity is 15.2056 m/s.
Next, let's calculate the change in velocity. Since Suzie comes to a stop, her final velocity is 0 m/s. The change in velocity is therefore:
Change in Velocity = Final Velocity - Initial Velocity
= 0 m/s - 15.2056 m/s
= -15.2056 m/s
Finally, we can calculate the average acceleration using the formula mentioned earlier:
Average Acceleration = Change in Velocity / Time
Let's plug in the values we've calculated:
Average Acceleration = -15.2056 m/s / 1.1 s
= -13.8232 m/s^2
Therefore, Suzie's average acceleration is approximately -13.8232 m/s^2. The negative sign indicates that her acceleration is in the opposite direction of her initial velocity.