# An object travels North at 5 m/s for 6 s and then travels South at 2 m/s for 4 s. What are the object's average speed and velocity?

Jul 2, 2016

Velocity is $0.3 \frac{m}{s}$
Speed is $0.7 \frac{m}{s}$

#### Explanation:

Effectively, velocity is just displacement divided by time, it doesn't matter how you go, it's how far from a point. So we'll find that later. Instead we will find the speed since speed is total distance by total time taken, or how long you keep going.

We'll keep memory that total time taken is $6 + 4 = 10 s = t$ for both cases since time is relevant to observation than calculation (you'll learn what this means in higher classes)

The total distance travelled by an object is $5 + 2 = 7 m = s$ (up 5m and then down 2m)
So, speed is $\frac{s}{t} = \frac{7}{10} = 0.7 \frac{m}{s}$

Velocity, that is different and for that I need you to visualize.
Imagine you have a rope tied to this object. The object moves 5m up and hence the length of this rope from you is now 5m. But then the rope again travels 2m south, down towards you. This makes the rope reduce in length by 2m. So that means the total length of the rope from your hand to the object is $5 - 2 = 3 m = x$ (notice we subtracted rather than added in speed)
So, velocity is $\frac{x}{t} = \frac{3}{10} \frac{m}{s} = 0.3 \frac{m}{s}$

So now you've come to realize why the velocity and speed are different. Main difference between the two is the definition, everything changes because of this.