6 (a) Which of these graphs represents an object moving with a constant velocity of 2 m/s? (1) (b) Figure 8 is a velocity/time graph showing a 34 s part of a train's journey - Edexcel - GCSE Physics - Question 6 - 2021 - Paper 1

To calculate the acceleration, we use the formula:
$a = \frac{v_f - v_i}{t}$
where:
v_f = final velocity (25 m/s),
v_i = initial velocity (5 m/s),
t = time (34 s).
Thus,
$a = \frac{25 - 5}{34} = \frac{20}{34} \approx 0.588$ m/s².
The acceleration of the train is approximately 0.59 m/s² when rounded to two significant figures.

The distance can be calculated using the formula:
$s = v_i t + \frac{1}{2} a t^2$
First, we calculate the distance using initial velocity and the observed acceleration.
Using initial velocity (5 m/s) and the calculated acceleration (approximately 0.588 m/s²):
$s = (5 \times 34) + \frac{1}{2} (0.588 \times 34^2)$
Calculating each term gives:
$s = 170 + 0.5 \times 0.588 \times 1156 \approx 170 + 340.1$
Thus, the total distance traveled is approximately 510.1 m, rounded to 510 m.

During the first few seconds after take-off, as the rocket engines produce a constant force, the acceleration of the rocket increases. This occurs because, as per Newton's second law (F = ma), when the force remains constant and the mass of the rocket decreases due to fuel consumption, the acceleration must increase. The decrease in mass occurs as fuel burns and is expelled, which in turn increases the acceleration of the rocket.