Question

a skateboarder is moving at a constant speed of 12 km/h along a flat surface. what would a distance - time graph of the skateboarders motion look like and how would the graph change if the skateboarder increases their speed to 14 km/h? record your response in the space provided.

Explanation:

Step1: Recall distance - time graph for constant speed

For a constant - speed motion, the distance - time graph is a straight line. The speed \(v=\frac{d}{t}\), where \(d\) is distance and \(t\) is time. When \(v = 12\ km/h\), the equation of the line is \(d = 12t\) (assuming the initial position is \(d = 0\) at \(t=0\)). The slope of the line is equal to the speed. So, the graph is a straight line with a slope of 12.

Step2: Analyze the change when speed increases

When the speed increases to \(v = 14\ km/h\), the new equation of the line is \(d = 14t\). The graph will still be a straight line, but it will have a steeper slope. Since the slope of a distance - time graph represents speed, a higher speed means a steeper line.

Answer:

The distance - time graph of the skateboarder moving at 12 km/h is a straight line with a slope of 12. When the speed increases to 14 km/h, the new distance - time graph is also a straight line, but it is steeper than the previous one because the slope of the new line is 14.