An athlete starts at point A and runs at a constant speed of 5.40 around a round track 150m in diameter.
Find the x component of this runner's average acceleration between points A and B.
I don't even know how to start.
Please help!
Where is points A and B?
To find the x component of the runner's average acceleration, we need to determine the change in the runner's velocity in the x-direction divided by the time it takes to travel from point A to point B.
Let's break down the problem into steps:
Step 1: Determine the time it takes for the runner to travel from point A to point B.
To find the time, we need to know the distance traveled and the constant speed of the runner. In this case, the distance traveled is the circumference of the circular track, which can be calculated using the formula C = 2πr, where r is the radius of the track. The radius, in this case, is half of the diameter given, so r = 150m/2 = 75m. Therefore, the circumference C = 2π * 75m.
Step 2: Calculate the time it takes to travel from point A to point B.
Since the runner is moving at a constant speed, we can use the formula time = distance/speed. The speed in this case is given as 5.40 m/s, and the distance is the circumference of the track. Thus, time = C / speed = (2π * 75m) / 5.40 m/s.
Step 3: Find the change in velocity in the x-direction.
Since the runner is moving in a circular path, their velocity is always tangential to the track. At point A, the velocity vector has no x-component. At point B, the runner has completed half of the circular track, so the velocity vector is pointing directly to the right (positive x-direction). Hence, the change in velocity in the x-direction is the component of the velocity vector at point B, which is equal to the runner's speed, 5.40 m/s.
Step 4: Calculate the x component of the average acceleration.
Now that we have the change in velocity in the x-direction and the time it takes to travel from point A to point B, we can calculate the average acceleration using the formula average acceleration = change in velocity / time.
Therefore, the x component of the runner's average acceleration between points A and B is 5.40 m/s divided by the time calculated in step 2.