ANSWER
• average velocity = 2.67 km/h = 0.742 m/s
,
• average speed = 5.33 km/h = 1.48 m/s
Step-by-step explanation
The average velocity formula is:
Where Δx is the displacement, which is the distance between the points A and B in a straight line. In this case there are 4 squares between each point, so the displacement of the man is 4km. Hence, the average velocity is:
![\bar{v}=\frac{4\operatorname{km}}{1.5h}=(8)/(3)(km)/(h)\approx2.67\operatorname{km}/h]()
The average speed is slightly different from average velocity, because we now have to consider the actual path taken by the man:
So the man didn't go from A to B in a straight line, but first he went 2km to the west, then 4km south and finally another 2 km east. In total, he went 8km. The average speed is:
![v_{\text{avg}}=\frac{8\operatorname{km}}{1.5h}=(16)/(3)(km)/(h)\approx5.33\operatorname{km}/h_{}]()
If we want the average velocity and speed in m/s we have to transform the units. We know that 1km is equivalent to 1000 m:
![1\operatorname{km}=1000m]()
First we can transform the km to m of each magnitude by multiplying and dividing by the same amount but in different units, like this:
![2.67(km)/(h)\cdot\frac{1000m}{1\operatorname{km}}=2670(m)/(h)]()
Note that the km units get cancelled. Now we have to transform from hours to seconds.
There are 3600 seconds in 1 hour:
As we did for the km, we can multiply and divide by the same amount in different units. We always put the unit we want to cancel in the opposite part of the fraction - in other words, we have hours in the denominator, so we have to put it in the numerator to get seconds:
The same process goes for the average speed. Now that we know we want to do both we can write them together:
![v_{\text{avg}}=5.33(km)/(h)=5.33(km)/(h)\cdot\frac{1000m}{1\operatorname{km}}\cdot(1h)/(3600s)=5.33\cdot(1000)/(3600)\cdot(m)/(s)\approx1.48(m)/(s)]()