Questions 51 & 52... Calculate Displacement & Calculate Velocity

51). Average Speed =
   (total distance biked) / (time to bike the distance)

   = (45 km + 45 km) / (4 hours)

   = (90 km) / (4 hours)

   = 22.5 km/hour

Displacement =

   the distance and direction from the start-point to the end-point,
   no matter what the route was from start to finish.

Our biker-babe started out from home and ended up at home.
The distance between home and home is zero.
Her displacement for the whole trip is zero.

52). First, there's the little problem of how long she took
in each direction.

   Return = Go + 0.5 hour

   Return + Go = 4 hours
   Return - Go = 0.5 hour

Add the two equations:

   2 x Return = 4.5 hours

Divide by 2: Return = 2.25 hours
    So Go = 1.75 hours.

(Check: Sum = 4 hours. Return is 1/2 hour more than Go. All OK.)

Now, finally . . .

   Velocity = (displacement + direction) / (time)

Going: Velocity = (45 km east) / (1.75 hours)

   = 25.71 km/hr east .

Returning: Velocity = (45 km west) / (2.25 hours)

   = 20 km/hr west .