Question

LiAn object is at t=25 at Xo = 3m and then t=45 at X=6m t=25 t=45 a. Find the average velocity ✓ b. Find x (t) if in this case the velocity is constant; for alt. t C. Graph xct)

Answer 1

a) Average velocity

Ū = 22-11 tr - ti 6 - 3 4 - 2 1.5 m/s

Positive sign indicates the direction of velocity vector is towards positive X-axis.

b) Velocity is constant, ${v}=1.5\,m/s$

Position $x(t)=x_1+v(t-2)$

(t) = 3 + 1.5(t - 2)

c) Graph of , position versus time is shown below.

1 position -0:5 0 0.5 1 time

d) $v(t)=\frac{dx(t)}{dt}=\frac{d}{dt}(1.5t)=1.5$

Graph of , velocity versus time is shown below.

velocity 3 2 -1- 0 5 10 time

e)

$a(t)=\frac{dv(t)}{dt}=\frac{d}{dt}(1.5)=0$

graph of acceleration versus time is shown below.
- 0:4 acceleration - 0-2- 2 3 time 0-2-

--------------------

2)

From the given graph,

Average velocity,

a) , $v=\frac{4-2}{3-0}=0.67\,m/s$

b) , $v=\frac{4-4}{4-3}=0\,m/s$

c)   ,$v=\frac{-4-4}{8-4}=-2\,m/s$

-------------------