A race finishes at the same place as it started. The contestants start from rest
ID: 2161294 • Letter: A
Question
A race finishes at the same place as it started. The contestants start from rest and cross the finish line running. Which one of the following is true about the average speed, the average velocity, and the average acceleration?
- average speed = 0 m/s, average velocity = 0 m/s, average acceleration = 0 m/s^2
- average speed not equal to 0 m/s, average velocity = 0 m/s, average acceleration not equal to 0 m/s^2
- average speed = 0 m/s, average velocity not equal to 0 m/s, average acceleration = 0 m/s^2
-average speed not equal to 0 m/s,average velocity not equal to 0 m/s,average acceleration not equal to m/s^2
-average speed not equal to 0 m/s, average velocity = 0 m/s, average acceleration = 0 m/s^2
I would like to say the second choice.
Explanation / Answer
When the runner has run a certain distance d, the average speed is the total length of the path taken divided by the time taken to run it: s=d/t. Average speed can only be zero if the runner does not run at all, in which case they cannot finish the race. So average speed is non-zero. Average velocity is a vector property which is the sum of the velocity (speed and direction) of the contestant at each step divided by the number of steps taken. The velocity vector can be thought of as an arrow pointing in the direction something is moving with a length equivalent to the distance it would travel in one second. These can be added by laying the arrows end to end without changing their directions (or turning them). Another way to look at it is to take the vector from the start of the race to the end of the race (a displacement vector) and divide by the time taken. Since the race starts and finishes in the same place, this must be zero. Average acceleration is also a vector property, and is the difference between the start velocity and the end velocity divided by the race time. It's the acceleration it would take to go from the initial velocity to the final velocity within the race time if the contestant were accelerating constantly throughout the race. This is dependant on the initial and final velocities of the runner and since they cross the finish line faster than when they started 'from rest', the average acceleration is non-zero. (p.s. slowing down is negative acceleration or 'deceleration') Thus the answer is b).