Question

Is acceleration a vector quantity or a scalar quantity?

Hint:

Check whether direction matters for this quantity, since acceleration comes from the rate of change of velocity.

Answer 1

Step 1: A quantity is called a vector if it needs both magnitude and direction to be fully described, and a scalar if magnitude alone is enough.

Step 2: Acceleration is defined as the rate of change of velocity with time, \( \vec{a} = \dfrac{\Delta \vec{v}}{\Delta t} \).

Step 3: Since velocity itself is a vector quantity, having both speed and direction, any change in velocity also has a direction associated with it. Dividing this change by time, which is a scalar, still leaves a quantity with direction.

Step 4: Acceleration can point in the same direction as velocity, causing speeding up, or opposite to it, causing slowing down, or even sideways, causing a change in direction. All of these describe different directions, which only makes sense for a vector.

Answer: Yes, acceleration is a vector quantity because it has both magnitude and direction.