Question

Why is velocity a vector whereas speed is a scalar quantity?
A. Velocity has both magnitude and direction and speed has only magnitude
B. Velocity has only magnitude and speed have both magnitude and direction
C. Velocity has both magnitude and direction and speed has only direction
D. Velocity has only direction and speed have both magnitude and direction

Answer 1

Hint: Distance is the actual length of the path covered. Vector quantities have both magnitude and direction.

Complete step by step solution:
Now if we compare their respective formulae, we have
Velocity(v) = $${\displaystyle \frac{Displacement}{Time}}$$ and Speed = $${\displaystyle \frac{Dis\tan ce}{Time}}$$
Now by definition we know that,
Distance is the actual length of the path covered. So, when you take a path with a lot of turns and curves, then the total length you cover is your distance.
Whereas
Displacement is the difference between the initial and the final positions of the path taken.

Now we take an example,
Suppose we are standing in a park. We move 30 meters forward, then take a right turn and go 10 meters in that direction. We take another right and then go forward for another 30 meters. Finally, we take another right and then walk 10 meters to come back to your original position (the path forms a rectangle with sides 30 and 10 meters).
Then by adding we get,
The total length of our path is
30+10+30+10 = 70 meters.

Our total distance covered is 70 meters. But our displacement is zero, as we come back to our original position.
Now suppose we say that we take 1 min to do this,
Then
Our speed would be =$${\displaystyle \frac{70}{1}}$$
= 70 meters/minute (or 1 meter/sec).

Now,
Our velocity would be 0 meters/minute (or 0 meters/sec).
We can conclude that
Velocity has both magnitude and direction that is why it is a vector quantity.
Whereas,
Speed has only magnitude and no direction that is why it is a scalar quantity.

Therefore, the correct option is A.

Additional information:
Scalar quantities:
Scalar quantities have only magnitude and no direction.
For example, 11 m and 15 m/s are both scalar quantities.
Scalar quantities change when their magnitude changes.
Vector quantities:
Vector quantities have both magnitude and direction.
For example, 11 m east and 15 m/s at 30° to the horizontal are both vector quantities.
Vector quantities change when:
1. their magnitude changes
2. their direction changes
3. their magnitude and direction both change

Note: Students must keep in mind that the velocity is zero because our displacement vector is zero.
It would be negative if we had negative displacement. In such a case, we would go much behind our starting point than in the forward direction (if we take starting point as 0, every meter ahead it as positive and every meter behind a negative).
So a positive or a negative sign helps us understand our direction. Hence it is a simplified version of a vector here.