Question 1: A car travels along a straight road. Its distance from a starting point is plotted against time, resulting in a graph. If the graph shows a straight line sloping upwards, what does this tell you about the car's speed?

Answer: The car is moving at a constant speed.

Question 2: On a distance-time graph, what does a flat (horizontal) section indicate about the motion of the object?

Answer: The object is stationary.

Question 3: Plot the graph of the function y=2x for x values from 0 to 5. Use the grid below to draw the line.

Answer: Graph of y=2x from x=0 to x=5

Question 4: A cyclist's distance from her starting point increases steadily for 10 minutes, then remains constant for 5 minutes before decreasing. Describe what the distance-time graph would look like.

Answer: A rising straight line for 10 mins, flat line for 5 mins, then a descending line.

Question 5: A train accelerates from rest, then moves at constant speed, then decelerates to a stop. Sketch the shape of this distance-time graph and explain the key features.

Answer: An initial curved (growing steepness) section for acceleration, a straight line for constant speed, and a curved section with decreasing steepness for deceleration.

Question 6: If a graph shows a steep upward slope, then a gentle slope, then a flat line, identify and explain what each part represents about the object's motion.

Answer: Steep slope: high speed; gentle slope: lower speed; flat: stationary.

Question 7: A vehicle's distance from a point is plotted over time. The graph shows an initial increase, then a decrease, then again an increase. What real-world scenario could this represent?

Answer: A vehicle moving away, then turning back towards the start, then moving away again.

Question 8: Identify and correct the mistake: A student draws a distance-time graph with a downward sloping line, claiming it shows the object moving away from the starting point.

Answer: Downward slope indicates decreasing distance; object is moving back toward start, not away.

Question 9: A bus travels at a constant speed of 60 km/h. How far does it travel in 2 hours? Show your working.

Answer: Distance = speed × time = 60 × 2 = 120 km

Question 10: A runner accelerates uniformly for 8 seconds, then maintains a constant speed. Sketch and describe the shape of their distance-time graph.

Answer: An initial curved segment indicating acceleration, followed by a straight line representing constant speed.

Question 11: Compare two objects: Object X has a steep upward slope, Object Y has a gentle slope. Which object is moving faster and why?

Answer: Object X is moving faster because its graph has a steeper slope.

Question 12: Design a challenging problem involving multiple features of distance-time graphs and solve it.

Answer: Answers will vary; expect multi-step reasoning involving interpretation of flat, steep, and curved sections, plus calculations of average speed.