## Statement

difficulty

Assuming that the following vector magnitudes refer to rectilinear motion, give their corresponding scalar representation:

•
• $∆\stackrel{\to }{r}=-3·\stackrel{\to }{j}m$
•
• $\stackrel{\to }{v}=3·t·\stackrel{\to }{i}m/s$

## Solution

Resolution

It represents the position vector of the motion. Remember that a vector has magnitude and direction. In this case:

• Magnitude: 3
• Direction: same as the unit vector $\stackrel{\to }{i}$

Movements that take place in the direction of the unit vector $\stackrel{\to }{i}$ are those associated with the x axis, therefore:

$∆\stackrel{\to }{r}=-3·\stackrel{\to }{j}m$

It is the displacement vector of the motion:

• Magnitude: 3 (magnitude is never negative)
• Direction: That given by the unit vector $-\stackrel{\to }{j}$

Movements that take place in the direction of the unit vector $\stackrel{\to }{j}$ are those associated to the y-axis, therefore:

It is normally written $\stackrel{\to }{v}=4·\left(-\stackrel{\to }{j}\right)=-4·\stackrel{\to }{j}$ .

Which is the velocity vector of the motion. Following a similar reasoning to the previous one:

$\stackrel{\to }{v}=3·t·\stackrel{\to }{i}m/s$

In this case the velocity vector of the motion depends on time. We can write:

• Magnitude 3·t
• Direction: given by the unit vector $\stackrel{\to }{i}$

The vector is associated to x-axis, therefore:

We haven't found any remarkable formula in this exercise.