CWatters said:The equation for a straight line is y=mx + c where m is the slope and c is a constant.
On your graph y is distance in meters, x is time in seconds so the slope is the velocity.
The slope of the line between two points (x1, y1) and (x2, y2) can be calculated from (y2-y1)/(x2-x1) or in English.. the change in y divided by the change in x... or the change in distance divided by the change in time.
BruceW said:that would be correct if the slope was constant throughout. But in this case it is not. You need to calculate the gradient of the slope at t = 4.
BruceW said:yes, that is the right answer :)
The way I like to think of it is like this: between t=3 and t=5, the person (or whatever it is) moves 5 meters, so he moves 5 meters in 2 seconds. So during this time, his average velocity is 2.5m/s and since his velocity is the same during this time, this is also equal to his instantaneous velocity.
Fishingaxe said:This answer I got apperently was wrong.
(15 - 10) / (5 - 3) = 5/2 = 2.5. is it 2.5m/s is the wrong answer for this problem.
My teacher said to find out the Instantaneous velocity in t=4.0s I should do it like this. In the time range 2.5 s to 7.0 s, the speed is constant. Instantaneous velocity at t = 4.0 s is therefore equal to this constant speed.
We determine this by the slope. v = m / s = 1.7 m / s.
:s
PeterO said:Bruce in post #9 gave you the correct method, but (not surpisingly) could not read accurate values of displacement from your sketch graph.
While you can take the slope from the complete straight section of the graph - from time 2.5 -> 7.0, you can always take the slope from any part of that straight section.
As I said, the nature of the graph you posted makes it rather difficult to estimate actual values of displacement at various times. The real graph you were working from was presumably much easier to read accurately.
Instantaneous velocity is the rate of change of an object's position at a specific moment in time. It is the velocity at a specific instant, as opposed to average velocity which is calculated over a given time interval.
Instantaneous velocity can be calculated by taking the derivative of an object's position with respect to time. This can be done using calculus and involves finding the slope of the tangent line to the object's position-time graph at a specific point.
Average velocity is calculated over a given time interval and represents the overall change in an object's position. Instantaneous velocity, on the other hand, is the velocity at a specific moment in time and can vary greatly from the average velocity depending on the object's motion.
The unit of measurement for instantaneous velocity is distance per time, such as meters per second (m/s) or feet per second (ft/s). This unit is the same as that for average velocity, as both represent a rate of change in an object's position.
Instantaneous velocity is important because it allows us to understand an object's motion at a specific point in time. It can help determine an object's speed and direction at any given moment and is essential in studying the behavior of moving objects.