An automobile travels on a straight road for 42 km at 45 km/h. it then continues in the same direction for another 42 km at 90 km/h. (assume that it moves in the positive x direction.) a. what is the average velocity of the car during this 84 km trip?
b. what is it’s average speed?
c. graph x versus t and indicate how the average velocity is found on the graph?

a) The average velocity is v = (60 km/h ; 0)

b) The average speed is 60 km/h

Explanation:

The velocity is a vector that has a magnitude and direction. The average speed is the distance traveled over time without taking into account the direction of the motion.

a)The average velocity is calculated as the displacement over time:

v = Δx/Δt

where

v = velocity

Δx = final position - initial position = traveled distance relative to the center of the reference system.

Δt = final time - initial time (initial time is usually = 0)

We know that the displacement is 84 km but we do not know the time. It can be calculated from the two parts of the trip.

In part 1:

v = 45 km/h = 42 km / t

t = 0.93 h

In part 2:

v = 90 km/h = 42 km / t

t = 42 km / 90 km/h

t = 0.47 h

The time of travel is 0.47 h + 0.93 h = 1.4 h

The average velocity will be:

v = 84 km / 1.4 h = 60 km/h

Expressed as a vector in a 2-dimension plane:

v = (60 km/h; 0)

b) The average speed is calculated as the distance traveled over time. Note that in this case, the distance is equal to the displacement since the direction of the motion is always in one direction. But if the direction of the second part of the trip would have been the opposite to the direction of the first part, the displacement would have been 0 (final position - initial position = 0, because final position = initial position), then, the average velocity would have been 0. In change, the average speed would have been the distance traveled (84 km, 42 km in one direction and 42 km in the other) over time.

Then:

average speed = 84 km / 1.4 h = 60 km/h

c) see attached figure.    

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

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