Cheryl runs a race on a 400.0 m circular track. She starts running east of the starting line and then circles the track and falls, stopping 1.00 m west of the starting line. Her time is 80.0 s. What was her average velocity?
I know the correct answer is -1.25 x 10-2 m/s.
But for the life of me I don't understand how they came up with that.
Remember that velocity is a vector, and that average velocity is based upon the total displacement (divided by time), not the distance covered.
She ends up one meter behind where she started. If displacement is positive towrds the east (the starting dorection), her displacement is -1.0 meter. Dividing by the time of 80 s, you get
Vav - -1.0/80 = -1.25*10-2 m/s
To find Cheryl's average velocity, we can use the formula:
Average velocity = total displacement / total time
In this case, Cheryl's total displacement is the distance between her starting point and where she stops, which is 1.00 m to the west of the starting line.
The total time is given as 80.0 s.
So, average velocity = -1.00 m / 80.0 s = -0.0125 m/s
When we express this in scientific notation, we get -1.25 x 10^-2 m/s.
Therefore, Cheryl's average velocity is -1.25 x 10^-2 m/s.
To find Cheryl's average velocity, we need to divide the total displacement by the total time taken.
The displacement is the change in position from the starting line to where Cheryl stops. In this case, she stops 1.00 m west of the starting line.
The time taken is given as 80.0 s.
Now, let's break down the problem and calculate the displacement and average velocity step by step:
1. Calculate the total distance Cheryl runs:
Since she starts east of the starting line and runs around the circular track before falling, we can consider her total distance as the circumference of the circular track. The formula for the circumference of a circle is C = 2πr, where r is the radius.
Given the track's circumference, C, is 400.0 m, we can find the radius, r, using the formula r = C / (2π):
r = 400.0 m / (2π) = 63.66 m (rounded to two decimal places)
So, the total distance Cheryl runs is the circumference of the circle, which is approximately 400.0 m.
2. Calculate the displacement:
Displacement is defined as the change in position from the starting point to the ending point. Since Cheryl stops 1.00 m west of the starting line, her displacement would be -1.00 m (negative because she's west of the starting line).
3. Calculate the average velocity:
Average velocity is the displacement divided by the time taken.
Average velocity = displacement / time taken
Average velocity = -1.00 m / 80.0 s
Now, divide the displacement by the time:
Average velocity = -0.0125 m/s
The answer, rounded to the correct number of significant figures, is approximately -1.25 x 10^(-2) m/s. Note that the negative sign indicates that Cheryl's velocity is westward.