Question

16 numeric 1 point mouse’s position vs. time calculate the object’s velocity during the time interval from 0 to 15 seconds using the position versus time graph above. answer

Explanation:

Step1: Recall velocity formula

Velocity \( v \) is the change in position (\( \Delta x \)) divided by the change in time (\( \Delta t \)), so \( v=\frac{\Delta x}{\Delta t} \).

Step2: Determine \( \Delta x \) and \( \Delta t \)

From the graph, at \( t = 0 \) s, position \( x_1 = 0 \) m. At \( t = 15 \) s, since the graph is linear from 0 to 15 s (up to 15 s, it's the same as up to 15 s in the 0 - 15 s interval, and at \( t = 15 \) s, the position should be the same as the linear part. Wait, actually, from 0 to 15 s, the graph goes from (0,0) to (15, 30)? Wait no, looking at the graph, at \( t = 15 \) s? Wait the graph has a point at \( t = 15 \)? Wait the graph: at \( t = 0 \), \( x = 0 \); at \( t = 15 \) s? Wait the graph's first segment is from (0,0) to (15? Wait no, the graph shows at \( t = 15 \) s? Wait the graph has a horizontal line starting at \( t = 15 \)? Wait no, the graph: the first line is from (0,0) to (15? Wait the graph's x - axis is time (s), y - axis is position (m). The first segment is from (0,0) to (15? Wait the graph has a point at \( t = 15 \)? Wait the graph: at \( t = 0 \), \( x = 0 \); at \( t = 15 \) s, looking at the graph, the first line goes up to \( t = 15 \) s? Wait no, the graph shows that at \( t = 15 \) s, the position is 30 m? Wait the graph: from \( t = 0 \) to \( t = 15 \) s, the position goes from 0 to 30 m? Wait the graph's first segment is from (0,0) to (15, 30)? Wait no, the graph has a point at \( t = 15 \) s? Wait the graph: the first line is from (0,0) to (15, 30)? Wait the graph's x - axis: 0, 10, 20, 30, 40. The first line is from (0,0) to (15, 30)? Wait no, the graph's first segment is from (0,0) to (15, 30)? Wait the graph: at \( t = 15 \) s, the position is 30 m? Wait the graph's first line is from (0,0) to (15, 30)? Wait \( \Delta x=x_2 - x_1=30 - 0 = 30 \) m, \( \Delta t=t_2 - t_1=15 - 0 = 15 \) s.

Step3: Calculate velocity

Using \( v=\frac{\Delta x}{\Delta t}=\frac{30 - 0}{15 - 0}=\frac{30}{15}=2 \) m/s.

Answer:

2 m/s