Agirl rolls a marble across the floor and determines the distance rolled (in meters) every second for 10 seconds. what is the average speed of the marble as it rolls across the floor? a. 0 m/sb. 0.67 m/sc. 1.5 m/sd. 150 m/s

The average speed of the marble as it rolls across the floor is 1.5 m/s.

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

The average speed of the marble can be gotten by finding the slope of the graph. The graph passes through (0, 0) and (6, 9).

The slope is:

The average speed of the marble as it rolls across the floor is 1.5 m/s.

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Average speed during some time interval =  

(distance traveled during the time) / (length of the time) .

According to the graph, the marble traveled 15 meters in 10 seconds.

Average speed = (15 m) / (10 s)

Average speed = 1.5 m/s during that 10 sec.  

We also know that the speed at any point in time is the slope of the graph at that point in time.  Since the graph is a straight line, it has the same slope at every point.  So the speed of the marble is 1.5 m/s at every instant during the 10 second interval.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west