Physics 5054/22 — May/June 2017

Walkthrough

The car starts from rest, so the initial speed $u = 0 \text{ m/s}$. It reaches a final speed $v = 25 \text{ m/s}$ in time $t = 14 \text{ s}$. With uniform acceleration, we use the kinematic equation $a = \frac{v - u}{t}$. Substituting the values gives $a = \frac{25}{14} = 1.7857... \text{ m/s}^2$, which rounds to $1.8 \text{ m/s}^2$ to two significant figures.

Key Takeaways

• The equation $a = \frac{v - u}{t}$ applies to uniform acceleration.
• Always remember that 'from rest' means $u = 0$.
• Round the answer to 2 or 3 significant figures as appropriate for the data given.

Common Mistakes

• Forgetting that 'from rest' means $u = 0$ and accidentally using $u = 25$ or $u = 14$.
• Swapping the numerator and denominator in the formula.
• Forgetting to include the unit $\text{m/s}^2$ in the final answer.

Things to Be Careful About

• The mark scheme accepts $25 / 14$ as the substitution step, so showing the formula with $u=0$ substituted is sufficient.
• Ensure the unit is written as $\text{m/s}^2$ and not $\text{m s}^{-2}$ to match 5054 conventions.

Walkthrough

The graph must show three distinct phases of motion:

1. 0 to 14 s: Uniform acceleration from rest to $25 \text{ m/s}$. On a speed-time graph, uniform acceleration is a straight line with a positive gradient. Draw a straight line from $(0, 0)$ to $(14, 25)$.
2. 14 s to 70 s: Speed continues to increase, but acceleration decreases. Decreasing acceleration means the gradient of the speed-time graph is decreasing. Draw a smooth curve from $(14, 25)$ up to $(70, 55)$ that is concave down (gradient gets flatter).
3. 70 s to 80 s: Constant speed of $55 \text{ m/s}$. Constant speed means zero acceleration, so the gradient is zero. Draw a horizontal straight line from $(70, 55)$ to $(80, 55)$.

Key Takeaways

• Gradient of a speed-time graph = acceleration.
• Straight line = uniform acceleration; curve with decreasing gradient = decreasing acceleration; horizontal line = constant speed (zero acceleration).

Common Mistakes

• Drawing a straight line for the second section instead of a curve with a decreasing gradient.
• Starting the constant speed section at the wrong time or wrong speed (must be $70 \text{ s}$ and $55 \text{ m/s}$).
• Not reaching exactly $25 \text{ m/s}$ at $14 \text{ s}$ for the first section.

Things to Be Careful About

• Read the graph axes carefully: time is $0-80 \text{ s}$ in steps of $20$, speed is $0-60 \text{ m/s}$ in steps of $20$.
• Ensure the curve is smooth and clearly shows a decreasing gradient; do not draw a jagged or straight line between $(14, 25)$ and $(70, 55)$.