Answer:
At 5 seconds, graph a shows a greater velocity. At 10 seconds, graph b shows a greater velocity.
Explanation:
In a distance-time graph, the slope of the curve corresponds to the velocity of the object. In fact, the slope of the curve is defined as:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
where [tex]\Delta y[/tex] is the variation of the y-variable and [tex]\Delta x[/tex] the variation of the x-variable.
In a distance-time graph, the y variable is the distance, while the x-variable is the time. Therefore, the slope of the curve corresponds to the ratio between the variation in distance and the variation in time:
[tex]m=\frac{\Delta s}{\Delta t}[/tex]
However, this is also the definition of velocity. Therefore:
- At 5 seconds, graph A has a greater slope, which means it shows a greater velocity than graph B
- AT 10 seconds, graph B has a greater slope, which means it shows a greater velocity than graph A
