4. (a) Which of these graphs represents an object moving with a constant velocity of 2 m/s? (1) (b) Figure 7 is a velocity/time graph showing a 34s part of a train's journey - Edexcel - GCSE Physics Combined Science - Question 4 - 2021 - Paper 1

To calculate the acceleration, we can use the formula:

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

From the graph, the initial velocity is 0 m/s at 0 s, and the final velocity is 20 m/s at 34 s. Thus:

$a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{34 \, \text{s}} = \frac{20}{34} \approx 0.588 \text{ m/s}^2$

Therefore, the acceleration of the train is approximately 0.59 m/s² (to two significant figures).

The distance can be calculated using the area under the velocity-time graph. The graph forms a trapezium:

1. Calculate the area:

   • Area of the trapezium = $\frac{1}{2} \times (b_1 + b_2) \times h$ where:
     • $b_1 = 0 \, \text{m/s}$ (initial velocity)
     • $b_2 = 20 \, \text{m/s}$ (final velocity)
     • $h = 34 \, \text{s}$ (time)

2. Plugging in the values:

$Area = \frac{1}{2} (0 + 20) \times 34 = 10 \times 34 = 340 \, \text{m}$

Thus, the distance the train travels is 340 meters.

During the first few seconds after take-off, the force produced by the rocket engines remains constant. However, as the rocket rises, it experiences a decrease in gravitational force acting against it.

Consequently, the net force acting on the rocket increases, leading to an increase in acceleration during the initial phase of the launch despite the thrust being constant. Over time, the acceleration may vary depending on the change in mass of the rocket due to fuel consumption.