Juan is on a morning jog. his speed is represented in the graph. at what rate of speed is juan running between 4min and 6min? according to this graph, what can you tell about juan's motion between 7min and 11min? if juan had maintained the same speed as in the first 7min, how long would it have taken him to run 3000m? explain your answer

a) The speed of Juan is 250 m/min

b) In that interval, he's at rest

c) Juan would have needed 12 minutes to run 3000 m

Explanation:

Distance vs Time Graph Analysis

If time is on the horizontal axis, and the distance is in the vertical axis, then the slope of the graph represents the instantaneous speed of the moving object. The graph shows three different zones which reflect Juan's jogging at that morning.

a) The period between 4 and 6 minutes clearly shows Juan is moving in such a way the distance increases when time passes. The speed of the motion can be obtained by computing the slope of the line. We can locate the points (4,1000) and (6,1500). We compute the speed  

The speed of Juan is 250 m/min

b) We can see between 7 and 11 minutes, Juan's distance is not changing because he stopped running. In that interval, he's at rest

c) We have already determined the speed on the first 7 minutes (the same as between 4 and 6 minutes). We know that

Where v is the speed, x is the distance, and t is the time

We need to know the time needed to travel x=3000 m at the initial speed v=250 m/min, so we solve the equation for t

Juan would have needed 12 minutes to run 3000 m

it has to be b, about 97 percent.

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