Suzie (of mass 76 kg) is roller-blading down
the sidewalk going 12 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 1.9 seconds.
What is Suzie’s average acceleration
Vo=12mi/h * 1600m/mi * 1h/3600s.=5.33m/s
a=(V-Vo)/t = (0-5.33)/1.9=-2.807 m/s^2.
To find Suzie's average acceleration, we need to use the formula:
Average acceleration = (Final velocity - Initial velocity) / Time
First, we need to convert Suzie's speed from miles per hour to meters per second, since the formula requires velocity in m/s.
1 mile = 1609.34 meters (approx)
1 hour = 3600 seconds
So, Suzie's speed in m/s is:
12 miles/hour * 1609.34 meters/1 mile * 1 hour/3600 seconds = 5.36 m/s
Now, we can substitute the values into the formula:
Average acceleration = (Final velocity - Initial velocity) / Time
Average acceleration = (0 m/s - 5.36 m/s) / 1.9 seconds
Simplifying the expression:
Average acceleration = -5.36 m/s / 1.9 s
So Suzie's average acceleration is approximately -2.82 m/s². The negative sign indicates that her acceleration is in the opposite direction of her initial velocity.
To calculate Suzie's average acceleration, we need to use the equation for acceleration:
acceleration = change in velocity / time
First, we need to convert Suzie's speed from miles per hour to meters per second because the SI unit for acceleration is meters per second squared.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, Suzie's speed in meters per second is:
12 miles/hour * 1609.34 meters/mile / 3600 seconds/hour = 5.36 m/s
Now, we can calculate the average acceleration using the equation mentioned earlier:
acceleration = (final velocity - initial velocity) / time
Here, initial velocity is 0 (since she makes a quick stop), final velocity is 5.36 m/s, and the time taken to stop is 1.9 seconds.
acceleration = (5.36 m/s - 0 m/s) / 1.9 s
acceleration = 5.36 m/s / 1.9 s
acceleration ≈ 2.82 m/s²
Therefore, Suzie's average acceleration is approximately 2.82 m/s².