University of Wisconsin Green Bay

You drive a car due north at a speed of 64 km/hr for 21 km, and then you accelerate to 96 km/hr and continue north for another 45 minutes. What is your average velocity?

  • In this problem, you are given information about the velocity, displacement, and time of a car over different legs of a trip, and asked for the average velocity. v, x, and t are all related through the definition of velocity, and so this is a definition problem.

    In general, if you are told about the rate at which some variable changes (in this case, x) you should check to see if you can work the problem just through the relevant definition.

  • Average Velocity

    There is no need for a picture in most definition problems. In this case, however, a picture may help you visualize the motion and understand the importance of using the definition equation to find your average velocity. It is not, however, required if you are comfortable with velocity. You are given distance, time and velocity information over two legs of a trip and asked for the average velocity of the entire trip. A picture will not provide any additional organization beyond what is already present in the problem.

  • In equation form, the definition of average velocity is given by

    This is the only relation you need for this problem.

  • Average Velocity

    At this point, you need to use the rest of the information given in the problem to find the distance covered in the second leg of the trip and the time required for the first leg of the trip:

    Average Velocity

    You can now return to the average velocity equation for the entire trip:

    Average Velocity

    The average velocity of the car is 86km/hr north. No further solution is needed.

  • Average velocity is one of the most frequently missed types of definition problem. Unless the object spends the same amount of time at each speed, you cannot just add the speeds and divide by two. Instead, you have to use the definition of average velocity, and divide the total distance covered by the car by the total amount of time required.

    Because the car spent more time traveling at 96 km/hr than it did traveling at 64 km/hr, it makes sense that the average speed is closer to 96 than to 64. Average velocity is the average speed and the direction, or 86 km/hr north.