Graphs in practical situations：練習問題

A car travels at a constant speed of \(60\text{ km/h}\). Which of the following represents the distance-time graph for this journey?

A water tank is being filled at a constant rate. Which sketch best represents the depth of water against time?

The kinetic energy \(E\) of an object is directly proportional to the square of its speed \(v\). When the speed is \(4\text{ m/s}\), the kinetic energy is \(32\text{ J}\). Which graph represents this relationship?

The speed-time graph shows a car accelerating uniformly from rest to a speed of \(20\text{ m/s}\) in \(5\) seconds. Calculate the acceleration of the car.

The speed-time graph for a train's journey shows it travelling at a constant speed of \(15\text{ m/s}\) for \(20\) seconds, then decelerating uniformly to rest over the next \(10\) seconds. Find the total distance travelled during this \(30\text{-second}\) interval.

The distance-time graph shown represents the motion of a car. Calculate the speed of the car, in km/h, during the first 2 hours of the journey.

A cyclist travels from home at a constant speed for 45 minutes until they reach a park 12 km away. After resting for 15 minutes, they return home along the same route at a constant speed of 24 km/h.

Calculate the total time, in minutes, for the entire journey from the moment they first leave home until they return.

A cyclist travels for $$20$$ seconds. For the first $$10$$ seconds, they accelerate uniformly from rest to a speed of $$5 \text{ m/s}$$. For the next $$10$$ seconds, they maintain this constant speed. Calculate the total distance covered by the cyclist.