An athlete springs a circular 400.0 m track in 50.0 s. Asume he runs a constant speed.

a. What is his speed over the entire course?
b. What is the magnitude of his instantaneous velocity at any point along the circuit?
c. If he starts facing west and runs counterclockwise, what is his velocity halfway around the circle?
d. What is the average acceleration for one lap of the track?

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a. His speed over the entire course is 400 meters divided by 50 seconds, which equals 8 meters per second. That's impressive, but I bet I could beat him on my unicycle!

b. The magnitude of his instantaneous velocity at any point along the circuit is also 8 meters per second. Although with my unicycle skills, I can reach a velocity of "falling-on-my-face" in no time!

c. If he starts facing west and runs counterclockwise, his velocity halfway around the circle would still be 8 meters per second, just in the opposite direction. So, he'd be heading east. I wonder if he stops for ice cream on the way?

d. The average acceleration for one lap of the track would be zero. Since the athlete is running at a constant speed, there is no change in velocity, and therefore no acceleration. Just like my brain when it comes to advanced calculus!

To answer these questions, we need to use the formulas related to circular motion. Let's go through each question step by step:

a. What is his speed over the entire course?
To find the speed, we can use the formula:
Speed = Distance / Time

In this case, the distance is the circumference of the circular track, which is given as 400.0 m. And the time taken to complete one lap is given as 50.0 s. Thus, we can calculate the speed as:
Speed = 400.0 m / 50.0 s = 8.0 m/s

Therefore, the athlete's speed over the entire course is 8.0 m/s.

b. What is the magnitude of his instantaneous velocity at any point along the circuit?
Since the athlete runs at a constant speed, the magnitude of his instantaneous velocity at any point along the circuit will also be equal to 8.0 m/s. The instantaneous velocity is the speed at a specific moment or position.

c. If he starts facing west and runs counterclockwise, what is his velocity halfway around the circle?
To find his velocity halfway around the circle, we need to consider both the speed and direction of the motion. Since he starts facing west and runs counterclockwise, halfway around the circle, he will be facing south.

The magnitude of the velocity remains the same, which is 8.0 m/s. However, the direction changes. Therefore, the velocity halfway around the circle is 8.0 m/s south.

d. What is the average acceleration for one lap of the track?
To find the average acceleration, we can use the formula:
Average Acceleration = Change in Velocity / Time

Since the athlete is running at a constant speed, there is no change in velocity, and thus the average acceleration will be zero.