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

To calculate the acceleration, we first need to determine the change in velocity and the time period.

From Figure 8, the initial velocity at 0 s is 0 m/s and the final velocity at 34 s is 25 m/s.

Using the formula for acceleration:

$a = \frac{\Delta v}{\Delta t}$
where ( \Delta v = v_{final} - v_{initial} = 25 - 0 = 25 ) m/s
and ( \Delta t = 34 ) s,

we find:

$a = \frac{25 \, \text{m/s}}{34 \, \text{s}} \approx 0.735 \text{ m/s}^2$

Rounding to 3 significant figures, the acceleration is approximately 0.735 m/s².

To calculate the distance traveled, we can use the formula for distance in uniformly accelerated motion:

$s = ut + \frac{1}{2}at^2$
where ( u = 0 \text{ m/s} ) (initial velocity), ( a \approx 0.735 \text{ m/s}^2 ), and ( t = 34 \text{ s} ).

Plugging in the values, we get:

$s = 0 \cdot 34 + \frac{1}{2} \cdot 0.735 \cdot (34)^2 \approx 0 + \frac{1}{2} \cdot 0.735 \cdot 1156 \approx 425.82 \, \text{m}$

Therefore, the distance the train travels in 34 s is approximately 426 m (to 3 significant figures).

During the first few seconds after take-off, the force produced by the rocket engines remains constant. According to Newton's second law, the relationship between force, mass, and acceleration is given by:

$F = ma$
If the force (F) remains constant and the mass (m) of the rocket decreases as fuel is burnt, then the acceleration (a) will increase. This is because as mass decreases for a constant force, the acceleration must increase to satisfy the equation, leading to a greater rate of change in velocity.