Youdriveoninterstate10fromsanantoni otohouston, half the time at 55 km/h and the other half at 90 km/h. on the way back you travel half the distance at 55 km/h and the other half at 90 km/h. what is your average speed
(a) from san antonio to houston,
(b) from houston back to san antonio, and
(c) for the entire trip?
(d) what is your average velocity for the entire trip?
(e) sketch x versus t for (a),
assuming the motion is all in the positive x direc- tion. indicate how the average velocity can be found on the sketch.

a)    Vm = 72.5 km / h   b) Vm = 72.5 km/h c) Vm = 0 km/h

Explanation:

The measured speed of a body is the ratio of the total distance traveled between the time taken.

a) Here they tell us that it goes from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h

   Let's look for the distance traveled

         V = x / t

         X1 = V1 t / 2

         X2 = V2 t / 2

The total distance the sum of the two distances

         Xt = X1 + X2

         Xt = V1 t / 2 + V2 t / 2

         Xt = (V1 + V2) t / 2

Let's calculate the average speed

         Vm = X / t

         Vm = [(V1 + V2) t / 2] / t

          Vm = (V1 + V2) / 2

           Vm = (55 +90) / 2

           Vm = 72.5 km / h

b) The return.

      Following the same procedure as part a

       Vm = (55+ 90) / 2

       Vm = 72.5 km / h

c)    go and return

The total distance to go and return is zero, since it returns to the starting point, which implies that the measured speed is zero

              Vm = 0 km / h

d) Same as part c

e) See attachments, in this case we can add the vectors directly, since the positions are read in the graph

With the slope of the line you can calculate the speed,

To find the average speed we can draw a line from the starting point to the end, read the distance and divide by the time read

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

happy to

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