Question

se the graph to determine the velocity of the object.

What is the instantaneous velocity of the object at 3 seconds?

m/s

What is the average velocity of the object?

m/s

Answer 1

I don't see the graph — could you upload it or tell me the position (or velocity) values at some times? Once I have the graph or numbers I can compute the requested velocities.

While you get that to me, here are the exact methods I'll use so you know what to expect:

- If the graph is position vs. time (x vs t):
- Instantaneous velocity at t = 3 s is the slope of the tangent to the x(t) curve at t = 3: v(3) = dx/dt|_{t=3}. If you only have the plot, approximate by drawing (or computing) a tangent line and finding its rise/run, or numerically approximate v(3) ≈ [x(3+Δt) − x(3−Δt)]/(2Δt) for a small Δt (e.g. 0.1 s).
- Average velocity over a time interval [t1,t2] is (x(t2) − x(t1)) / (t2 − t1). If you mean the average over the entire shown interval, use its endpoints.

- If the graph is velocity vs. time (v vs t):
- Instantaneous velocity at t = 3 s is simply the value v(3) read off the curve.
- Average velocity over an interval [t1,t2] (or over the whole shown interval) equals the displacement divided by time = (1/(t2−t1)) ∫_{t1}^{t2} v(t) dt — graphically, area under the v(t) curve between t1 and t2 divided by (t2−t1). For the whole interval [0,T] average = (area under curve from 0 to T)/T.

If you upload the graph or give the relevant coordinates/values (position at several times or velocity values), I’ll calculate the instantaneous velocity at 3 s and the average velocity and show the work.