Question

A flea walking along a ruler moves from the 45 cm mark to the 27 cm mark.What is the displacement? What is the speed? (Define increasing numbers to be the positive direction and decreasing numbers to be the negative direction.)

Answer 1

Question (a)

The displacement is equal to

$\Delta \vec{X}=\vec{X_{f}}-\vec{X_{i}}$

Where

• Final position $\vec{x_{f}}=27cm$
• Initial position $\vec{x_{i}}=45cm$

Evaluating numerically.

$\Delta \vec{X}=27cm-45cm=-18cm$

Displacement is

$\boxed{\Delta \vec{X}=-18cm}$

Question (b)

The speed is equal to:$V=\frac{d}{t}$

Where

• Distance traveled (Displacement module) $d=|\Delta \vec{x}|=18cm$
• The time is: $t=??$

The problem time is not given, but it is if one considers that t = 2s then, the speed is:

$V=\frac{18cm}{2s}=9\frac{cm}{s}$

Now if you were asked to calculate the velocity then you should use the equation

$\vec{v}=\frac{\Delta \vec{x}}{t}$

Where

• Displacement $\Delta \vec{x}=-18cm$
• the time is $t=??$

In this case the sign is maintained, and if it is calculated using t = 2s it has to.

$\vec{v}=\frac{-18cm}{2s}=-9\frac{cm}{s}$

Note: It takes a time where the displacement occurs to calculate speed and velocity, but here are two examples.