Question

the chart shows danielas run through her race. what is her velocity? 1.5 m/s 2 m/s 2.5 m/s 5 m/s

Explanation:

Step1: Recall the formula for velocity

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

Step2: Identify initial and final positions and times

From the graph, at \( t_1 = 0 \) s, the position \( x_1 = 5 \) m. At \( t_2 = 10 \) s, the position \( x_2 = 29 \) m (approximate from the graph, but let's check the slope). Wait, actually, let's take two points. Let's use \( t = 0 \), \( x = 5 \) and \( t = 10 \), \( x = 29 \)? Wait, no, maybe better to see the slope. The line goes from (0,5) to (10,29)? Wait, no, the y - axis at t = 10 is around 29? Wait, no, maybe the final position at t = 10 is 29? Wait, no, let's recalculate. Wait, the formula for the slope of a position - time graph is velocity. The slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \) (here x is time, y is position). So let's take two points: (0,5) and (10,29)? Wait, no, maybe the correct points: when t = 0, x = 5; when t = 10, x = 29? Wait, no, let's check the difference. Wait, maybe the final position at t = 10 is 29? Wait, no, let's do it properly. Let's take \( t_1 = 0 \) s, \( x_1 = 5 \) m; \( t_2 = 10 \) s, \( x_2 = 29 \) m? Wait, no, the graph at t = 10, the position is 29? Wait, no, maybe I made a mistake. Wait, the y - axis is position in meters. At t = 0, x = 5. At t = 10, x = 29? Wait, no, let's calculate the slope. The change in position \( \Delta x=x_2 - x_1 \), change in time \( \Delta t=t_2 - t_1 \). Let's take \( t_1 = 0 \), \( x_1 = 5 \); \( t_2 = 10 \), \( x_2 = 29 \)? Wait, no, maybe the correct points: let's see, the line starts at (0,5) and goes to (10,29)? Wait, no, the difference in position is \( 29 - 5=24 \), difference in time is \( 10 - 0 = 10 \), so velocity would be \( \frac{24}{10}=2.4 \), close to 2.5. Wait, maybe the final position at t = 10 is 30? Wait, if at t = 10, x = 30, then \( \Delta x=30 - 5 = 25 \), \( \Delta t=10 - 0 = 10 \), so \( v=\frac{25}{10}=2.5 \) m/s.

Step3: Calculate velocity

Using the formula \( v=\frac{\Delta x}{\Delta t} \). Let \( x_1 = 5 \) m (at \( t_1 = 0 \) s) and \( x_2 = 30 \) m (at \( t_2 = 10 \) s). Then \( \Delta x=x_2 - x_1=30 - 5 = 25 \) m, \( \Delta t=t_2 - t_1=10 - 0 = 10 \) s. Then \( v=\frac{25}{10}=2.5 \) m/s.

Answer:

2.5 m/s (the option: 2.5 m/s)