Question

On a distance time graph like the one shown here, the slope represents the ______ of the car.

displacement


velocity


acceleration


color

Answer 1

The slope of a distance-time graph is SPEED ... just like it says in the title of the graph, at the top. Note: It's NOT velocity ... the graph tells nothing about the DIRECTION the car is moving at any time.

Answer 2

Speed

Step-by-step explanation:

The speed of an object is defined as the ratio between the distance covered by the object (d) and the time it takes for the object to cover that distance (t):

`v=(d)/(t)`

In a distance-time graph, we see that this quantity corresponds to the slope of the line. In fact, the slope of the line is

`m=(\Delta y)/(\Delta x)`

where
`\Delta y` is the increment in the y-variable and
`\Delta x` is the increment in the x-variable. However, we see that the y-variable corresponds to the distance, while the x-variable corresponds to the time interval, so the slope is equivalent to the ratio between the distance covered and the time taken, which corresponds to the speed.

Note that this is different from velocity, which is a vector, therefore it also includes the direction of motion: however, in the graph the direction is not specificed, so we can only infere the speed of the car.