# Can velocity be positive with a negative displacement? Explain please :)

Mar 7, 2017

Yes see explanation

#### Explanation:

There are two types of quantities, and it is important to know the difference;

1) Scalar quantities. These have magnitude ie. size only .
For example: temperature.

2) Vector quantities, these have BOTH size and direction.

to show the difference:

Consider an object moving North $5 m {s}^{- 1}$

its speed is $5 m {s}^{- 1}$ and is a scalar

but its velocity of $5 m {s}^{- 1}$ North is a vector.

Now distance is as scalar, but displacement is a vector

so if an object starts at the origin and moves " "5 m" "  in the $+ x -$axis then$\text{ " 10 m " }$in the opposite direction, it ends up at$\text{ " -5m " }$from the origin.

it has moved a distance of $\text{ "15m" }$

but its displacement is $\text{ "-5m." }$

if we use vector notation:

the object goes:$\text{ } 5 \vec{i} - 10 \vec{i} = - 5 \vec{i}$

So displacement can be negative.

at this point the object can move with a velocity of, say, $\text{ } 2 \vec{i} m {s}^{- 1}$
so an object can have positive velocity and negative displacement

In fact the constant acceleration equations can be written into vector form, thus taking all of this into account.