Explain why velocity is a vector but speed is not
Take note that a scalar quantity has magnitude only. While vector quantity has magnitude and direction.
Speed is the rate at which an object covers a specified distance. It is a scalar quantity since direction is not necessary. For example, if a person runs 2 kilometers in an hour, his speed is 2 kph. It does not matter if he runs on a straight road or on a circular path.
Velocity is a vector quantity. Take note note that velocity is defined as the rate at which an object changes its position. So, it not only measures how fast the object is moving, but its starting point and end position are considered. The magnitude of its motion should be accompanied with its direction. For our example above, let's add direction to it. If the person runs 2 km on a circular path, it means that he returns to its original position. Since there is no change in its initial and final position, then his velocity is 0. On the other hand, if he runs 2 kilometers on a straight road going east for an hour, then his velocity is 2kph east.
Both velocity and speed have the same units of measurement for example (meters per second). So it is understandable that no difference is apparent.
However velocity represents displacement over time, while speed represents distance over time.
Displacement is a vector, meaning, displacement may be stated as say 3 meters to the south or it has both magnitude (3m) and direction (south).
Distance is a scalar, meaning, scalar may be stated as 15 meters, or it contains only information for the magnitude (15m), no direction.
Time is a scalar since it only has magnitude and that too only in the forward direction.
Velocity arises from a vector (displacement) while speed arises from a scalar (distance), hence Velocity is a vector (magnitude and direction) and speed is a scalar (magnitude only).
When measuring speed the direction of travel is not taken into account. For that reason you can be travelling toward any destination, whether it be positive or negative in your frame of reference, and it still be a positive speed. This is due to the fact that speed is a scalar quantity and not a vector. Speed also only shows the amount of distance being covered in a certain time, and distance is never negative.
Velocity however IS a vector quantity thus it can denote a positive or negative direction on a given plane. You can be travelling at a speed greater than 0 but be travelling in a negative direction. While distance can never be negative, direction can be in your frame of reference.
The dictionary definition of this difference as I learned it is that velocity has “both magnitude and direction” whereas speed “only has magnitude”. This is the reason why velocity is a vector but speed is only a scalar value. An easier way I found to digest this information is to think about it in terms of an example. Say you are driving a car on the number line (which has a very clear designation of positive being “more right” and negative being “more left). In that case, if you start at the 0 point on the number line and drive to -5 in 1 second, your displacement is -5 – 0, or -5 units. Divided by the time of 1 second, your velocity is -5 units/second. However, because you travelled a distance of 5 meters in 1 second, your speed is 5 units/second. From this, you can clearly see how velocity has a direction (in that it can be a positive or a negative value) whereas even when velocity is negative, speed is positive (hence why it is scalar – because it is always positive).
Speed is a scalar quantity which comprises of magnitude only whereas velocity is a vector quantity which comprises of magnitude and direction. Speed is like 12 m/s, this is magnitude, and is expected to move in one direction whereas 12 m/s in northeast direction has a magnitude of 12 and direction northeast that is 45`@`
Velocity and speed are pretty much the same thing. However, velocity has direction while speed does not. For instance, I could say that my car is moving 30 m/s, which is an example of speed. But if I say that my car is going 30 m/s south, than that makes it an example of velocity because you are giving the direction. And since vectors deal with directions themselves, velocity is a vector and speed is not.