# kinematics question (1 Viewer)

#### somerandomperson

##### New Member
A car moves from point A to point B along a straight line. The car passes the first third of the distance with a constant velocity v1. The second third of the distance the car travels with a constant velocity v2 and for the last third of the distance the car moves with a velocity v3. What is the magnitude of its average velocity?

I got confused on how to come up with an expression for average velocity, anyone know how?

#### blyatman

##### Well-Known Member
Let $\bg_white d$ be the total distance travelled. Now $\bg_white x = vt$, so $\bg_white t = x/v$

The time spent in each section is therefore:
$\bg_white t_1=\frac{d/3}{v_1}$
$\bg_white t_2=\frac{d/3}{v_2}$
$\bg_white t_3=\frac{d/3}{v_3}$

The average velocity is simply the total distance divided by the time taken:
$\bg_white \bar{v}=\frac{d}{t_1+t_2+t_3}$

The variable $\bg_white d$ should cancel out from the above expression, leaving you with a final answer solely in terms of the given velocities.

Goddamn I'm bored at work.

#### CM_Tutor

##### Moderator
Moderator
And hence,
$\bg_white \bar{v}=\cfrac{3}{\cfrac{1}{v_1}+\cfrac{1}{v_2}+\cfrac{1}{v_3}}$

#### Qeru

##### Well-Known Member
A car moves from point A to point B along a straight line. The car passes the first third of the distance with a constant velocity v1. The second third of the distance the car travels with a constant velocity v2 and for the last third of the distance the car moves with a velocity v3. What is the magnitude of its average velocity?

I got confused on how to come up with an expression for average velocity, anyone know how?