Question

Scenario

Answer 1

(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, $m s^{-2}$). In fact, acceleration is defined as

$a=\frac{\Delta v}{\Delta t}$

where $\Delta v$ is the change in velocity while $\Delta t$ is the change in time.

In the graph, we see that $\Delta v$ corresponds to the increment in the y-variable, while $\Delta t$ corresponds to the increment of the x-variable; so acceleration is also equal to

$a=\frac{\Delta y}{\Delta x}$

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.

Answer 2

Answer:

A) The car started with a velocity = 5 m/s at time t = 0 seconds, and finish it path (that means its velocity = 0 m/s) at t = 10 seconds.

If we draw this two points: (0,  5) and (10,  0) we get a line, where x-variable represents time in seconds and y-variable represents the velocity of the car (see picture attached).

B) The slope of the plot obtained in point A is calculated as follows:

slope =  (0 - 5)/(10 - 0) = -0.5

which represent the variation of velocity respect time, this is called acceleration. In this case, the acceleration is -0.5 m/s². The negative value indicates that the car is decreasing its velocity as time increase.