When would instantaneous speed be the same as average speed?
would it be
when the speed is constant?
when the position changes linearly with time
or would it be in the limit when the time interval goes to zero?
I thought it would be when the speed is constant, but i'm not sure...I've tried looking in my textbook but cannot find the answer
To determine when instantaneous speed would be the same as average speed, let's break down the options you provided:
1. When the speed is constant: In this case, the instantaneous speed would indeed be equal to the average speed. This is because the speed remains the same throughout the entire time period, resulting in a constant rate of motion.
2. When the position changes linearly with time: If the position changes linearly with time, it implies that the object is undergoing uniform motion. In this scenario, both the instantaneous speed and the average speed would be the same. This is because the object covers equal distances in equal time intervals, resulting in a constant average speed.
3. In the limit when the time interval goes to zero: This refers to taking the instantaneous speed as the time interval approaches zero. In this case, the instantaneous speed would be the same as the average speed if the object is moving at a constant speed. However, if the object's speed is changing, the instantaneous speed and the average speed may differ.
In summary, both the options of having a constant speed and the position changing linearly with time would result in the instantaneous speed being the same as the average speed. However, the third option of taking the limit as the time interval goes to zero depends on the nature of the object's motion. If the speed is constant, then the instantaneous speed would be equal to the average speed in this limit.