# Speed and Velocity

Speed is the distance an object moves in a certain time: speed = distance/time.

In this figure, Clone A has negative displacement (-2m) and positive velocity (to the right). Clone B has positive displacement (+2m) and negative velocity (to the left). This means that in time, the displacement of A will increase, while t

The units of speed are typically km/h or m/s. Speed is only the magnitude (scalar value) of the motion.

Recall that displacement is a vector. This means it tells us two pieces of information: distance and direction. In a similar way, velocity is a vector, and tells us two things: the speed of an object and the direction it is going in.

In this graph, we see that an object has different displacements at different times. It starts at zero (origin) and moves at a velocity of +2m/s (in a positive direction at a speed of 2m/s) for two seconds.

Then it stays still for four seconds, before moving again with positive velocity of +1m/s for 4 seconds, before staying at rest for two seconds.

From this graph we can see that its final displacement is +8m from the origin.

Let us now see what this movement looks like as a velocity-time graph:

When the object is at rest, velocity is zero, and when it is moving, velocity is greater than zero.

To calculate the displacement we need to find the area under the velocity-time graph.

For constant velocity, the area under the graph is displacement = velocity x time.

For constantly changing velocity, the graph is a triangle, so the area under the graph can be calculated using the Pythagoras Theorem.

The area under the graph is the velocity of an object multiplied by the time the object moves for:

\$\$d = v⋅t\$\$

### The Maths

In the example above: \$d = d_1 + d_2\$, where \$d_1\$ is the displacement in the first two seconds, and \$d_2\$ is the displacement in the time period 6 - 10 seconds. Note that when v = 0, d = v⋅t = 0.

∴ \$d_{total} = d_1 + d_2 = v_1⋅t_1 + v_2⋅t_2 = 2 ⋅ 2 + 1 ⋅ 4 = 4 + 4 = 8\$ m.

In this example, we have written the time interval for which the object travelled as 't'. More correctly, we should say it is 'change in time', which uses a special symbol: Δ (delta).

We could write the above equation as: change in position (displacement) = velocity x change in time:

Mathematically, this looks like: \$Δd = v ⋅ Δt\$.

Note that we do not say Δv, because the velocity in this case is constant, and therefore not changing.

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