# Speed vs Velocity

Show/Hide Sub-topics (Speed, Velocity and Acceleration | O Level)

To understand the difference between speed and velocity, you will need to grasp the difference between distance and displacement, which can be found here.

Speed is the distance moved per unit time.

• SI unit is metre per second ($m \, s^{-1}$)
• Scalar quantity
• Equation: $\text{Speed} \, = \, \frac{d}{t}$, where d is distance travelled and $t$ is time taken
• Average speed, $\left< \text{speed} \right>$ can be calculated using $\frac{\text{total distance travelled}}{\text{total time taken}}$
• Instantaneous speed is the speed at any instant
1. Measured by a speedometer

Velocity (v) of an object is the rate of change of displacement with respect to time.

• SI unit is metre per second ($m \, s^{-1}$)
• Vector quantity
• The magnitude of velocity is speed
• $v = \frac{s}{t}$, where s is displacement and $t$ is time taken
• Average velocity, $\left< v \right>$ can be calculated using $\frac{\text{total displacement}}{\text{total time taken}}$

As velocity is a vector quantity, you have to specify its magnitude and direction to completely describe it.

## Examples

### A boy ran a distance of 100 metres in 11.32 seconds. What was his average speed?

From above, we have:

\begin{aligned} \left< \text{speed} \right> &= \frac{\text{total distance travelled}}{\text{total time taken}} \\ &= \frac{100}{11.32} \\ &= 8.83 \text{ m s}^{-1} \end{aligned}

### A car travels 5 km due east and makes a U-turn back to travel a further distance of 3 km. The car completes the journey in 0.3 hours.

Find:

1. the distance covered;
2. the displacement of the car;
3. the average speed;
4. the average velocity.

(a) The distance covered is $5 + 3 = 8 \text{ km}$.

(b) The displacement is $5 -3 = 2 \text{ km due east of the starting point}$.

(c)

\begin{aligned} \left< \text{speed} \right> &= \frac{\text{total distance travelled}}{\text{total time taken}} \\ &= \frac{8}{0.3} \\ &= 26.7 \text{ km h}^{-1} \end{aligned}

(d)

\begin{aligned} \left< v \right> &= \frac{\text{total displacement}}{\text{total time taken}} \\ &= \frac{2}{0.3} \\ &= 6.67 \text{ km h}^{-1} \text{ due east of starting point} \end{aligned}

## Self-Test Questions

### What is the difference between speed and velocity?

Speed is a scalar while velocity is a vector.

Speed is a rate of change of distance while velocity is the rate of change of displacement.

### For an object that is moving at a constant velocity, is it necessary for it to be moving in a straight line?

Velocity is a vector quantity – both magnitude and direction are accounted for. For an object to have constant velocity, it is necessary that both the magnitude and the direction of the velocity vector be kept constant. If either magnitude or direction is changing, the velocity will not remain constant.

Hence, for an object to have a constant velocity, it is necessary for it to be moving in a straight line at a constant speed.

On the other hand, speed can remain constant if direction is changed and magnitude is kept constant, as speed is a scalar quantity.

### 11 thoughts on “Speed vs Velocity”

2. A student walks at a constant speed. He takes 100sec to walk 160paces. The length of each pace is 0.80m.
How far does the student walk in 50sec?

• Don’t we need to change km to m and hour to second? since si unit for distance is m and time is s ?or thats okay to use km and hour?

• 100s divide by 2 is 50sec and 160 divide by wo is 80 times 0.80=64

• two* sorry that was error

• The distance will be 39.0625