Define (i) velocity, (ii) acceleration - Leaving Cert Physics - Question a - 2008

Acceleration is defined as the change in velocity with respect to time. It can be expressed as:

$a = \frac{v - u}{t}$

where:

• $a$ is the acceleration,
• $v$ is the final velocity,
• $u$ is the initial velocity,
• $t$ is the time taken.

The velocity-time graph consists of three distinct segments:

1. From 0 to 10 seconds, the velocity increases linearly from 0 to 20 m/s.
2. From 10 to 15 seconds, the velocity remains constant at 20 m/s.
3. From 15 to 19 seconds, the velocity decreases linearly back to 0 m/s.

It can be plotted as follows:

• X-axis: Time (seconds)
• Y-axis: Velocity (m/s)

The points representing the journey are:

• (0,0)
• (10,20)
• (15,20)
• (19,0)

The graph has straight lines connecting these points.

From the graph, at 6 seconds, the velocity can be estimated to be: 12 m/s.

Using the formula for acceleration:

$a = \frac{v - u}{t}$

Substituting the known values:

• $v = 20$ m/s (final velocity),
• $u = 0$ m/s (initial velocity),
• $t = 10$ s,

the calculation becomes:

$a = \frac{20 - 0}{10} = 2 \, \text{m/s}^2$.

When the boat is moving at a constant velocity of 20 m/s for 5 seconds, the distance can be calculated using:

$d = vt$

Substituting the known values:

• $v = 20$ m/s,
• $t = 5$ s,

we find:

$d = 20 \, \text{m/s} \times 5 \, \text{s} = 100 \, \text{m}.$

Thus, the distance travelled at constant velocity is 100 m.