Solving Velocity Vectors on a Graph

[roadrunner]

Homework Statement

im given a graph. the graph itself isn't so important though

it is a curve, with 3 point vectors going from the origin to 3 points on the path of motoion of the particle.

they are at t=2.6, 2, 2.4

a and b) I am asked to draw the average velocity vectors of the particle over t=2 and t=2.4
and also over t=1.5 and t=2

c) write an expression for the velocity vecotr v(2)

d) draw an approximation to the vector v(2) and estimate the speed of the particle and v(2)

Homework Equations

The Attempt at a Solution

a and b
is it just...draw a line form the point t=2.4 and t=2
and for b from t=1.5 to t=2

and that's the average velocity vector?

c) do i use the formula

lim     r(2+h)-r(2)
h-->0       h

d) NO CLUE!?

 

[roadrunner]

i think for D i guess based on looking at the slope?
so in my case it looks like a slope of -1
so the speed would be -1? (or 1)

 

[chaoseverlasting]

The average velocity is total distance by total time, so a and b are correct. For c, the equation of a line is given by Z=mX+c where m is the slope. In this case, m will be dx/dt or your average velocity.

Therefore, x=vt+c (here Z=x and X=t) and you can find the value of c by plugging in the position and time of anyone point that you are given. If you need the equation in vector form, its even easier, r(x,t)=(t2-t1)i+(x2-x1)j, here I am assuming that time is graphed on the x-axis and the distance on the y axis.

Now, the equation of the line in vector or cartesian form (z=mx+c is the cartesian form) when graphed gives you the approximation of the vector you desire. The speed of the particle is the magnitude of the velocity, aka, velocity without direction. You should be able to use the graph to figure it out...