How can we determine velocity from a position-time graph without using calculus?

[oldspice1212]

Hey guys, so I have a quick question about position - time graphs, so without using calculus for let's just say a particle moving west along a horizontal straight line every 0.10 s and the displacement is 0.022, 0.032, 0.042, etc.

Well the displacement from t = 0 aren't really good numbers that I used lol, but let's just assume it's non - linear, and without calculus would we just use a tangent line and find the slope of the tangent line to figure out velocity at what ever time interval we are given.


Thanks

 

[urbano]

I think that is correct, the slope at that particular point is your velocity.

 

[oldspice1212]

I think that is correct, the slope at that particular point is your velocity.

That's what I'm thinking but I wasn't certain.

 

[collinsmark]

Be careful. There are two different measures of velocity, and either one might be asked for, depending on the problem.

In both cases, assume that you already have a displacement vs. time curve.

• The tangent of any point on the curve gives you the instantaneous velocity. That's the velocity of the particle at a particular instant in time.
  
• But if you're given a particular time interval (meaning two, separate points on the curve), it usually means you are being asked to find the average velocity. For that, use
  
  $$\vec {v_{\mathrm{ave}}} = \frac{ \vec {\Delta s}}{\Delta t}$$
  where $\vec {\Delta s}$ is the change in displacement and $\Delta t$ is the change in time (i.e., the specified time interval).

[Edit: Instantaneous velocity and average velocity become equal when $\Delta t \rightarrow 0$, at time t, where the instantaneous velocity was measured, meaning the two points on the curve merge into each other to form a single point. Otherwise, instantaneous and average velocities are not necessarily equal.]

 

[Nickie]

for your question! Yes, you are correct. To determine velocity from a position-time graph without using calculus, we can use the slope of the tangent line at a given point. This slope represents the instantaneous velocity of the particle at that specific time. By finding the slope of the tangent line at different points along the graph, we can determine the velocity at different time intervals. However, it is important to note that this method will only give us the instantaneous velocity at a specific point in time, and not the average velocity over a given interval. To calculate average velocity, we would need to divide the total displacement by the total time taken. I hope this helps!