practice

  1. I went for a walk one day. I walked north 6.0 km at 6.0 km/h and then west 10 km at 5.0 km/hr. (This problem is deceptively easy, so be careful. Begin each part by reviewing the appropriate physical definition.) Determine …
    1. the total distance of the entire trip,
    2. the total displacement of the entire trip,
    3. the average speed of the entire trip,
    4. the average velocity of the entire trip, and
    5. the average acceleration of the entire trip.
  2. A swimmer heads directly across a river swimming at 1.6 m/s relative to still water. She arrives at a point 40 m downstream from the point directly across the river, which is 80 m wide. Determine …
    1. the speed of the river current,
    2. the magnitude of the swimmer's resultant velocity,
    3. the direction of the swimmer's resultant velocity, and
    4. the time it takes the swimmer to cross the river.
  3. A car enters an intersection at 20 m/s where it collides with a truck. The impact rotates the car 90° and gives it a speed of 15 m/s. Determine the average acceleration of the car if it was in contact with the truck for 1.25 s.
  4. Write something completely different.

conceptual

  1. At what direction (somewhat upstream, directly across, somewhat downstream) should you swim in order to cross a river …
    1. with the least displacement,
    2. in the least time?

numerical

  1. In the fictitious city of Metropolis, streets run east-west while avenues run north-south. The separation between centers for both the streets and the avenues is 100 m, resulting in square city blocks. Superman is located at 33rd Street and 3rd Avenue while Lois Lane is located north and east of Superman at 45th Street and 12th Avenue.
    1. How far would Lois Lane have to walk to reach Superman?
    2. How far would Superman have to fly to reach Lois Lane?
    3. In what exact direction should Superman fly to reach Lois Lane as quickly as possible?
  2. Calculate both the distance and the magnitude of the displacement of the earth after …
    1. one complete orbit,
    2. one-half of an orbit,
    3. one-fourth of an orbit, and
    4. one-eighth of an orbit around the sun.
    5. What relationship between distance and displacement does this verify?
  3. Calculate both the speed and the magnitude of the velocity of the earth after completing …
    1. one orbit,
    2. one-half an orbit,
    3. one-fourth an orbit, and
    4. one-eighth an orbit around the sun.
    5. What relationship between speed and velocity does this verify?

algebraic

  1. Given a straight river with parallel banks, flowing uniformly at speed vriver and a swimmer capable of speed vswim > vriver, at what angle (assuming that directly across is 0°) should the swimmer head in order to cross the river …
    1. with the least displacement,
    2. in the least time?