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 believe that it would be -1.25 x 10^-2 m/s, is this right?
She started "east" of the starting line. How far east?
If 0m east, she ran 399m/80s = 4.9875m/s
don't know where you got the negative velocity, unless you're calculating her falling speed. :-)
To find Cheryl's average velocity, we need to calculate the displacement and divide it by the time taken.
The displacement is the difference between Cheryl's final position and her initial position. In this case, Cheryl starts running east of the starting line and stops 1.00 m west of the starting line. Since she is running on a circular track, we can consider the displacement as the distance traveled along the circumference of the circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, since the track is circular, the circumference is equal to 400.0 m, the length of the track. Therefore, we can find the radius of the track using the formula:
C = 2πr
400.0 = 2πr
Solving for r:
r = 400.0 / (2π) ≈ 63.66 m
Now, we can calculate the displacement along the circle. Cheryl's displacement is the distance traveled plus the direction, which is west. Since she stops 1.00 m west of the starting line, her displacement is -1.00 m.
Next, we calculate the average velocity by dividing the displacement by the time. Cheryl's displacement is -1.00 m, and her time is 80.0 s.
Average velocity = displacement / time
Average velocity = -1.00 m / 80.0 s
Calculating the value:
Average velocity ≈ -0.0125 m/s
So, your answer of -1.25 x 10^-2 m/s is correct. Cheryl's average velocity is approximately -0.0125 m/s, or -1.25 x 10^-2 m/s.