# Q & A: vector kinematics

Q:
When vectors are written as "letters" or "symbols", they are typed as bold and italic lowercase letters and,in handwriting, indicated by a dash or a wavy line underneath them. I know that this is the convention. My question is regarding the kinematic equations of motion with constant acceleration: v2=u2+2as v=u+at & s=ut+(1/2)at2....ARE THE TERMS IN THESE EQUATIONS VECTORS OR SCALARS???! and if they are vectors, why do all text books simply show them as normal letters(neither italic nor bold)??? QUESTION 2: "these equations are used for motion in a straight line only".is this statement true? (P.S. i have absolutely no knowledge of motion in non-straight lines..so please keep your explaination simple) Thanks alot.
- Anonymous (age 16)
A:
As you noted, all those equations are only true when the acceleration "a" is a constant. If all the motion is along some particular line, you can treat the variables v (velocity), a, and s (displacement) as simple numbers describing motion along that line. You do have to be careful to describe one direction as positive and the other as negative and stick to that rule for each variable. The equations still work when v, a, and s are vectors, so long as "as" is taken to mean the vector dot product. When a and v aren't along the same line, then the direction of motion changes and the object follows a curving path. Maybe some textbooks don't use vector notation because they are trying to introduce the simpler case first.

Many interesting types of motion (e.g. circular orbits) are not described by these equations because a isn't constant.

Mike W.

(published on 12/22/2010)

## Follow-Up #1: vector or scalar

Q:
So, just to be sure, you mean that as long as the motion is in one particular straight line it does not matter whether the terms are written with vector notation or not; and these equations are still valid when v and a etc are in different directions...right?
- same person who asked the question (age 16)
A:

Unless v and a are along the same line, the overall motion won't be along a single line. So in that case you have to use vector notation, and the product is the vector dot product. If they are along the same line, then you don't need the vector notation.

Mike W.

(published on 12/26/2010)