Suzie (of mass 58 kg) is roller-blading down
the sidewalk going 36 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 2
.
4 seconds.
What is Suzie’s average acceleration?
Answer in units of m
/
s
2
009 (part 2 of 3) 1.0 points
What force was exerted to stop Suzie?
Vo=36mi/h * 1600m/mi * 1h/3600s=16 m/s.
V = Vo + a*t = 0
16 + a*2.4 = 0
2.4a = -16
a = -6.67 m/s^2.
F = m*a = 58 * (-6.67) = -386.7 N.
The negative sign means that the force was in the opposite direction of the motion.
To find Suzie's average acceleration, we need to first convert her speed from miles per hour to meters per second.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, 36 miles per hour is equal to:
36 miles/hour * 1609.34 meters/mile / 3600 seconds/hour = 16.09 m/s
Now, we can calculate the average acceleration using the formula:
Average acceleration = Change in velocity / Time taken
Given that Suzie came to a stop from a moving position, her initial velocity is 16.09 m/s and her final velocity is 0 m/s. The time taken to stop is 2.4 seconds.
Average acceleration = (0 m/s - 16.09 m/s) / 2.4 s
Average acceleration = -16.09 m/s / 2.4 s
Average acceleration = -6.704 m/s^2
So, Suzie's average acceleration is -6.704 m/s^2 (negative because she is decelerating).
To calculate the force exerted to stop Suzie, we need to use Newton's second law of motion, which states:
Force = mass * acceleration
Given that Suzie's mass is 58 kg and her acceleration is -6.704 m/s^2, we can calculate the force:
Force = 58 kg * (-6.704 m/s^2)
Force = - 388.432 kg·m/s^2
The force exerted to stop Suzie is approximately -388.432 kg·m/s^2. The negative sign indicates that the force is acting in the opposite direction to her motion.
To calculate Suzie's average acceleration, we can use the formula:
Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)
First, we need to convert Suzie's speed from miles per hour to meters per second.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, Suzie's speed becomes:
Speed = 36 miles per hour * (1609.34 meters / 1 mile) * (1 hour / 3600 seconds)
Next, we calculate the change in velocity by subtracting her initial velocity (which is 0 because she stopped) from her final velocity (which is the speed we just calculated):
Δv = Final velocity - Initial velocity
= Speed - 0
= Speed
Now, we can plug in the values into the formula:
Acceleration (a) = Δv / Δt
= Speed / Time taken
= Speed / 2.4 seconds
After calculating that, you will have the value for Suzie's average acceleration in meters per second squared (m/s^2).
To calculate the force exerted to stop Suzie, we need to use Newton's second law of motion:
Force (F) = Mass (m) * Acceleration (a)
Given that Suzie's mass is 58 kg (as stated in the question) and we have already calculated the acceleration, we can now calculate the force exerted to stop Suzie by multiplying her mass by the acceleration.
Force (F) = Mass (m) * Acceleration (a)
= 58 kg * (value of acceleration obtained above)
After performing the calculation, you will have the value for the force exerted on Suzie in units of Newtons (N).