Define (i) velocity and (ii) acceleration - Leaving Cert Physics - Question a - 2018

Acceleration is defined as the change in velocity per unit time, represented mathematically as:

$a = \frac{\Delta v}{t}$

where $\Delta v$ is the change in velocity and $t$ is the time taken.

Using the formula for acceleration:

$a = \frac{\Delta v}{t}$

we rearrange to find $t$:

$t = \frac{\Delta v}{a}$

Substituting in, we have:

$t = \frac{55\, \text{m s}^{-1}}{0.4\, \text{m s}^{-2}} = 137.5\, \text{s}$

To calculate the distance travelled at top speed, we use the formula:

$d = v \times t$

Substituting in:

$d = 55\, \text{m s}^{-1} \times 300\, \text{s} = 16500\, \text{m}$

The graph can be illustrated as follows:

• The graph starts at the origin (0,0).
• From time 0 to 137.5 seconds, the velocity increases linearly from 0 m/s to 55 m/s due to acceleration.
• From 137.5 seconds to 437.5 seconds, the velocity remains constant at 55 m/s.

The correct shape of the graph should resemble a triangle followed by a horizontal line.