12. Answer any two of the following parts (a), (b), (c), (d) - Leaving Cert Physics - Question 12 - 2008

Acceleration is the rate of change of velocity with respect to time. It signifies how quickly an object is speeding up or slowing down. The formula used to calculate acceleration is:

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

where:

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

To create the velocity-time graph of the boat's journey:

1. Start from a point at (0, 0) since the speedboat starts from rest.
2. After 10 seconds, plot a point at (10, 20) as the boat reaches 20 m s⁻¹.
3. Continue horizontally from (10, 20) to (15, 20) for the next 5 seconds as the boat maintains this velocity.
4. Finally, plot a point at (19, 0) as the boat comes to a stop after 4 seconds.

The resulting graph will show a line rising to 20 m s⁻¹ at 10 seconds, remaining constant at that level for 5 seconds, and then declining to 0 over 4 seconds.

From the velocity-time graph, at 6 seconds, the velocity of the speedboat is approximately 12 m s⁻¹. This is determined by drawing a vertical line from the time axis at 6 seconds to intersect the velocity line.

To calculate the acceleration during the first 10 seconds:

Using the formula for acceleration:

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

Substituting the values:

• Final velocity ($v$) = 20 m s⁻¹,
• Initial velocity ($u$) = 0 m s⁻¹,
• Time ($t$) = 10 s:

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

Thus, the acceleration of the boat during the first 10 seconds is 2 m/s².

To calculate the distance travelled while the boat was moving at constant velocity:

Distance can be calculated using the formula:

$s = v \cdot t$

where:

• $v$ is the constant velocity (20 m s⁻¹),
• $t$ is the time duration (5 seconds).

Substituting the values:

$s = 20 \, \text{m/s}^{-1} \cdot 5 \, \text{s} = 100 \, \text{meters}$

Thus, the distance travelled by the boat while moving at constant velocity is 100 meters.