Question

speed problems
match the graph that best fits the motion from the data table.

time (sec)	distance (m)
5	15
10	30
15	45
20	60

Explanation:

Step1: Calculate the speed

Speed $v=\frac{\Delta d}{\Delta t}$. For the first - time interval from $t = 0$ s to $t = 5$ s, $v=\frac{15 - 0}{5-0}=3$ m/s. For the interval from $t = 5$ s to $t = 10$ s, $v=\frac{30 - 15}{10 - 5}=3$ m/s. For the interval from $t = 10$ s to $t = 15$ s, $v=\frac{45 - 30}{15 - 10}=3$ m/s. For the interval from $t = 15$ s to $t = 20$ s, $v=\frac{60 - 45}{20 - 15}=3$ m/s. The speed is constant.

Step2: Analyze the graph types

A constant - speed motion has a linear distance - time graph with a non - zero slope. The first graph is a non - linear (curved) graph which represents non - constant speed. The second graph has a zero slope (horizontal line), which means the object is at rest. The third graph has a negative slope, which means the object is moving in the opposite direction. The fourth graph is a straight line starting from the origin with a positive slope, which represents a constant positive speed.

Answer:

The fourth graph (the straight - line graph with a positive slope starting from the origin)