Question

why is it important to describe both magnitude and direction of a quantity such as velocity

Answer 1

The reason it is important is to determine various quantities in physics such as acceleration and momentum, that very much depend not only on the magnitude of velocity, but also on the direction.

For example, in uniform circular motion, the speed is constant while the direction is always changing, resulting in an acceleration whose direction is pointed inward toward the center of some circle.

Answer 2

Use a car traveling north. That is a vector with direction only. But it doesn't quantify anything. If you said the car was traveling north at 60 mph, now you have velocity and direction and you can now add the vectors to get a resultant that makes sense.

Answer 3

@RANE Physics is also like or a part of mathematics.

1)Sometimes, the direction of a number or quantity is as important as the number itself.

2)Vector quantities have both a magnitude and a direction.

3) For e.g:- A Man is driving a car at the rate of 30 km/h , we know that that man drives at the rate of 30 km/h and if we mention direction also , that information will become more efficient,accurate and appropriate also.

That's why , it is important to describe both magnitude and direction of a quantity .

Answer 4

Hope you understand.

Answer 5

@mayankdevani i know that Vector quantities have both a magnitude and a direction.
but i need it explain this in more detailed in terms of motion

Answer 6

Look at velocity, which has magnitude and direction. Notice how the vector \(\overline r(t)\) is changing, but only in direction:
$$
\overline r(t)=a\hat{x}(t)+b\hat{y}(t)\\
\overline {v(t)}=\cfrac{d }{d(t)}\overline r(t)
$$

If we write \(\overline r(t)\) in polar form:
$$
\large{
\vec r=R\hat u_R(t)\\
\vec v = \frac {d}{dt} \vec r(t) = \frac {d R}{dt} \hat u_R + R\frac {d \hat u_R } {dt} \
}
$$
Where
$$
\large{
\frac {d \hat u_R } {dt} = \frac {d \theta } {dt} \hat u_\theta \
}
$$
Measures how the velocity vector is changing in direction.

In uniform circular motion, this is the only component of the velocity vector that is changing, because:
$$
\large{
\frac {d R}{dt} \hat u_R =0
}
$$
Which indicates that the Radius is constant (in uniform circular motion).



This relates the magnitude and direction of the velocity vector to motion.

Answer 7

That's the basic difference between a scalar and a vector quantity. Speed has no direction and it is scalar, there is no fixed direction of speed.

But Velocity is a vector quantity , so along with the speed the direction should also be specified in order to describe the velocity properly.

Answer 8

Ok .. i would like to offer my simple explanation

if i tell you
i and you put a force of 50 N each on that table right there.. and ask you.. hey what happens to that table? can you describe its motion? how much acceleration it gets maybe?

what is your answer?

Next .. you ask me where am i .. and i say.. hey i am exactly 50 meters from your house.. would i have answer your question? would u kno my position?

Suppose you are to do radio traffic control of two planes.. both pilots tell you they are going with lets say 500m/s and 300m/s.. your job is to make sure they don't bump into each other.. are those data sufficient?

All of them are missing one important info DIRECTION.. and its not like you can say.. Oh just the direction is missing.. the information is SOOOO USELEESSSS .. you can't do ANYTHING without the info of the direction in my examples..

so do you understand now why we couple directions along with some physical quantities and make them vectors..?