(a) Graph is attached
The velocity-time graph for the cart is attached.
On the x-axis, time is represented in seconds (s).
On the y-axis, velocity is represented in metres per second (m/s).
Since the cart travels constantly at 5 m/s, its velocity remains the same, so it is represented as a flat line, until a time of 10 seconds.
(b) The slope of the graph representes the acceleration
In a velocity-time graph, the slope of the graph represents acceleration (which is measured in metres per second square, [tex]m s^{-2}[/tex]). In fact, acceleration is defined as
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
where [tex]\Delta v[/tex] is the change in velocity while [tex]\Delta t[/tex] is the change in time.
In the graph, we see that [tex]\Delta v[/tex] corresponds to the increment in the y-variable, while [tex]\Delta t[/tex] corresponds to the increment of the x-variable; so acceleration is also equal to
[tex]a=\frac{\Delta y}{\Delta x}[/tex]
which is the slope of the graph. In this particular case, the line is flat: this means that the slope is zero, so the acceleration is zero.
