IB Physics Average Speed Problems

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A tutorial sheet on average speed problems.

  1. A car travels at 50 km h-1 for a distance of 150 km and then travels at 30 km h-1 for another 150 km. What is the average speed for the entire trip?
  2. A car travels to a town at an average speed of 40 km h-1. The return journey on the same road is made with an average speed of 30 km h-1. Find the average speed for the entire journey.
  3. Two identical planes Mike and Ike race against each other. They start at the same place and both have an air speed of v km h-1. A wind from the east of w km h-1 blows, w < v. The planes start at the same point and time. Mike travels to a point d km east on the ground and returns. Ike travels to a point d km north on the ground and returns. Show that the average speed of Mike is (v2 - w2)/v and the average speed of Ike is (v2 - w2)1/2.
  4. Show that Ike always wins the race. Hint (v2 - w2)1/2 < v, v2 - w2 < v(v2 - w2)1/2. This problem is taken from Relativity for the Layman by James A Coleman, 1958, pp 32-33 and the solution is given in The Physics Teacher, vol 34, Oct 1996, pp 438-439.