Motion and Motion Graphs: Physics 0625 (Cambridge O Level / IGCSE)

A distance–time graph is plotted for a runner during a training session. From $t = 0$ to $t = 8\text{ s}$, the graph is a straight line and the distance increases steadily from $0\text{ m}$ to $96\text{ m}$. From $t = 8\text{ s}$ to $t = 20\text{ s}$, the graph is a horizontal straight line at a distance of $96\text{ m}$. What is the runner's speed during the first $8\text{ s}$, and what does the second section of the graph show about her motion?

A student travels from home to school. She first walks $400\text{ m}$ to a bus stop, taking $300\text{ s}$. She then waits at the bus stop for $100\text{ s}$ before the bus arrives. Finally, she travels $4500\text{ m}$ on the bus to school, taking $300\text{ s}$.

(a) Calculate the total distance she travels and the total time taken for the whole journey (including the time spent waiting), and use these to calculate her average speed for the whole journey. [3]

(b) On a distance–time graph for this journey, state what feature of the graph would be seen during the $100\text{ s}$ she spends waiting at the bus stop, and explain why the graph has this feature. [2]

(c) As the bus pulls away from the stop, the distance–time graph for this part of the journey is a curve that gets steeper and steeper for the first $10\text{ s}$, before becoming a straight line. State whether the bus is accelerating or decelerating during this first $10\text{ s}$, and explain how you can tell this from the shape of the graph. [2]

A speed–time graph is recorded for a car during a short test on a straight, flat road. The graph has three straight-line sections:

• From $t = 0$ to $t = 8\text{ s}$: the speed increases steadily from $0\text{ m/s}$ to $20\text{ m/s}$.
• From $t = 8\text{ s}$ to $t = 20\text{ s}$: the speed stays constant at $20\text{ m/s}$.
• From $t = 20\text{ s}$ to $t = 24\text{ s}$: the speed decreases steadily from $20\text{ m/s}$ to $0\text{ m/s}$.

(a) State what the straight, sloping line between $t = 0$ and $t = 8\text{ s}$ shows about the way the car's speed is changing during this section. [1]

(b) Calculate the distance travelled by the car during the first section, from $t = 0$ to $t = 8\text{ s}$, by finding the area between the graph and the time axis. [2]

(c) Calculate the distance travelled by the car during the second section, from $t = 8\text{ s}$ to $t = 20\text{ s}$. [2]

(d) Calculate the total distance travelled by the car for the whole $24\text{ s}$ test, from $t = 0$ to $t = 24\text{ s}$. [3]

A delivery drone flies in a straight line. Its speed at different times is shown below.

After $t = 20\text{ s}$, the drone speeds up again. From $t = 20\text{ s}$ to $t = 30\text{ s}$, the speed–time graph for the drone is a curve that becomes less steep as time goes on (rather than a straight line).

(a) Calculate the acceleration of the drone during the first phase, from $t = 0$ to $t = 5\text{ s}$. [2]

(b) State the acceleration of the drone during the second phase, from $t = 5\text{ s}$ to $t = 15\text{ s}$, and explain your answer. [2]

(c) Calculate the acceleration of the drone during the third phase, from $t = 15\text{ s}$ to $t = 20\text{ s}$. State whether your answer represents an acceleration or a deceleration, and explain how the sign of your answer shows this. [3]

(d) State what the shape of the graph during the fourth phase (from $t = 20\text{ s}$ to $t = 30\text{ s}$) shows about the drone's acceleration, and explain how you can tell this from the graph. [2]

A distance–time graph shows two hikers, P and Q, who start walking from the same point at the same time. Hiker P's line is a straight line from $(0\text{ s}, 0\text{ m})$ to $(40\text{ s}, 240\text{ m})$. Hiker Q's line is a straight line from $(0\text{ s}, 0\text{ m})$ to $(40\text{ s}, 160\text{ m})$. Which hiker is walking faster, and what is the difference between their speeds?

A cyclist sets off from her house and rides in a straight line to a park, stops to rest, then rides back home along the same route. Her distance from home is recorded throughout the journey:

• From $t = 0$ to $t = 300\text{ s}$: her distance from home increases steadily from $0\text{ m}$ to $1500\text{ m}$.
• From $t = 300\text{ s}$ to $t = 420\text{ s}$: her distance from home stays constant at $1500\text{ m}$.
• From $t = 420\text{ s}$ to $t = 570\text{ s}$: her distance from home decreases steadily from $1500\text{ m}$ back to $0\text{ m}$.

(a) Calculate the cyclist's speed during the first section of the journey, from $t = 0$ to $t = 300\text{ s}$. [2]

(b) State what the cyclist is doing between $t = 300\text{ s}$ and $t = 420\text{ s}$, and explain how you can tell this from the graph. [2]

(c) Calculate the cyclist's speed during the final section of the journey, from $t = 420\text{ s}$ to $t = 570\text{ s}$. [2]

(d) Explain how the graph shows that, during this final section, the cyclist is travelling back towards home rather than continuing to travel further away from home. [1]

A hot air balloon pilot practises controlling the balloon's height during a short test flight over flat ground. The balloon's height above the ground is recorded throughout the flight:

• From $t = 0$ to $t = 40\text{ s}$: the height increases steadily (a straight line on the graph) from $0\text{ m}$ to $300\text{ m}$.
• From $t = 40\text{ s}$ to $t = 100\text{ s}$: the height continues to increase steadily (a straight line, but with a shallower gradient) from $300\text{ m}$ to $480\text{ m}$.
• From $t = 100\text{ s}$ to $t = 160\text{ s}$: the pilot begins a controlled descent. The height decreases from $480\text{ m}$ to $120\text{ m}$, but this section of the graph is a curve, not a straight line: it is steep immediately after $t = 100\text{ s}$ and becomes less steep as $t$ approaches $160\text{ s}$.

(a) Calculate the balloon's ascent speed during the first section, from $t = 0$ to $t = 40\text{ s}$. [2]

(b) Calculate the balloon's ascent speed during the second section, from $t = 40\text{ s}$ to $t = 100\text{ s}$. State which of the two ascent sections has the greater speed, and explain how this is shown by the steepness of the two lines. [2]

(c) State whether the balloon's descent speed during the third section is constant, increasing, or decreasing, and explain how you can tell this from the shape of the graph. [2]

(d) Calculate the balloon's average descent speed for the whole third section, from $t = 100\text{ s}$ to $t = 160\text{ s}$. Explain why this value is not equal to the balloon's actual descent speed at every instant during this section. [3]

(e) Calculate the total distance travelled by the balloon (vertically) during the whole $160\text{ s}$ flight described above. [1]

A speed–time graph is recorded for a skateboarder riding down a ramp and then braking. From $t = 0$ to $t = 4\text{ s}$, her speed increases steadily from $2\text{ m/s}$ to $10\text{ m/s}$. From $t = 4\text{ s}$ to $t = 6\text{ s}$, she brakes, and her speed decreases steadily from $10\text{ m/s}$ to $0\text{ m/s}$. What is the magnitude of her acceleration while braking, and how does it compare with the magnitude of her acceleration during the first $4\text{ s}$?

A train travels between two stations in a straight line. Its distance from the first station is recorded every so often, and the distance-time graph between each pair of readings is a straight line:

(a) Calculate the train's speed during the first section of the journey, from $t = 0$ to $t = 20\text{ s}$. [2]

(b) State which section of the journey shows the train at rest, and explain how you can tell this from the table. [2]

(c) Calculate the train's speed during the section from $t = 50\text{ s}$ to $t = 70\text{ s}$, and its speed during the section from $t = 70\text{ s}$ to $t = 90\text{ s}$. [3]

(d) The train is approaching the second station at the end of the journey. State whether the train is speeding up or slowing down between the section in (c) covering $t = 50\text{ s}$ to $t = 70\text{ s}$ and the section covering $t = 70\text{ s}$ to $t = 90\text{ s}$, and explain your answer. [1]

(e) Calculate the train's average speed for the whole $90\text{ s}$ journey shown in the table. [2]

A skydiver jumps from a stationary hot air balloon and falls vertically before opening her parachute. Her speed at various times after jumping is shown in the table below:

(a) Calculate the skydiver's acceleration during the first second of the fall, from $t = 0$ to $t = 1\text{ s}$, and compare your answer with the acceleration of free fall, $g \approx 9.8\text{ m/s}^2$. [2]

(b) Show that the skydiver's acceleration between $t = 4\text{ s}$ and $t = 6\text{ s}$ is smaller than her acceleration between $t = 0$ and $t = 1\text{ s}$. [3]

(c) State the term used for the speed the skydiver reaches after $t = 10\text{ s}$, and explain, in terms of the forces acting on her, why her speed stops increasing at this point. [3]