Question

sara is investigating how different surfaces affect a toy cars ability to maintain a constant speed. she sets up a 10 - meter track and uses a tin measure how long it takes the car to travel each 2 - meter segment. she tests the car on four different surfaces. here are her results:

on which surface does the car best maintain a constant speed? justify your answer using the data.

Explanation:

Step1: Recall the formula for speed

Speed \(v=\frac{d}{t}\), where \(d\) is distance and \(t\) is time. For a constant speed, the time \(t\) taken to cover equal - distance segments (\(d = 2m\) in this case) should be approximately the same.

Step2: Analyze the time data for each surface

• Wood: The times are \(1.0s\), \(1.0s\), \(1.0s\), \(1.1s\), \(1.1s\). There is a change from \(1.0s\) to \(1.1s\).
• Carpet: The times are \(1.2s\), \(1.3s\), \(1.4s\), \(1.5s\), \(1.6s\). The time is increasing steadily.
• Tile: The times are \(0.9s\), \(0.9s\), \(0.9s\), \(0.9s\), \(0.9s\). The time taken to cover each \(2 - meter\) segment is the same (\(t = 0.9s\)). Using \(v=\frac{d}{t}\) with \(d = 2m\), \(v=\frac{2}{0.9}\approx2.22m/s\) (constant value).
• Sandpaper: The times are \(1.3s\), \(1.5s\), \(1.7s\), \(1.9s\), \(2.1s\). The time is increasing steadily.

Since the time taken to cover each \(2 - meter\) segment is constant (\(t = 0.9s\)) for the tile surface, by the formula \(v=\frac{d}{t}\), the speed of the car on the tile surface is constant.

Answer:

The car best maintains a constant speed on the tile surface.