Define (i) velocity and (ii) acceleration - Leaving Cert Physics - Question 12 - 2018

Acceleration is defined as the rate of change of velocity with respect to time. It is also a vector quantity. The formula for acceleration is:

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

where ( \Delta v = v_f - v_i) is the change in velocity and ( \Delta t) is the change in time. Acceleration is measured in meters per second squared (m/s²).

Using the formula for acceleration: $a = \frac{v_f - v_i}{t}$ Given that the train starts from rest ( (v_i = 0 m/s)) and accelerates to a top speed of (v_f = 55 m/s) at an acceleration of (0.4 m/s²):

$t = \frac{v_f - v_i}{a} = \frac{55 - 0}{0.4} = 137.5 \, \text{seconds}$

The distance travelled at top speed can be calculated using the formula: $d = v \times t$ where ( v = 55 m/s ) and ( t = 300 , seconds ). Thus:

$d = 55 \times 300 = 16500 \, meters$

The velocity-time graph consists of three sections:

1. A straight line increasing from the origin to a top speed of 55 m/s over 137.5 seconds, indicating acceleration.
2. A horizontal line at 55 m/s for 300 seconds, indicating constant speed.
3. The graph should conclude after the total time taken for both acceleration and constant speed, properly labeling the axes as 'Time (s)' and 'Velocity (m/s)'.