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How to Calculate Average Velocity with Displacement & Speed?

  1. Nov 24, 2014 #1
    1. The problem statement, all variables and given/known data
    A car travels 14.6 km west at a speed of 40 km/h, then travels 12.0 km south at a speed of 50 km/h and finally travels 19.0 km east at a speed of 45 km/h. What is the magnitude of the average velocity for the car over the entire trip?

    2. Relevant equations
    3 kinematics equations?

    3. The attempt at a solution
    Not sure where to start., or where to go from there.
     
  2. jcsd
  3. Nov 24, 2014 #2
    Also, please help solve this problem:

    A car travels 15.6 km west at a speed of 40 km/h, then travels 11.4 km south at a speed of 50 km/h and finally travels 11.3 km east at a speed of 45 km/h. What is the average speed for the car over the entire trip?

    It's the same thing, EXCEPT it is asking for average speed, not the average velocity as in the original question.
     
  4. Nov 25, 2014 #3
    Regarding how to begin these types of problems:
    It is useful to list all known variables, and all possible equations; this allows you to analyze the environment.

    Regarding the first question:
    Consider that velocity is a vector: it possesses a direction and a magnitude; consider the influence of this condition upon your answer for average velocity.

    Consider that the velocity is equal to the ratio of distance traveled per unit of time: therefore, the average velocity is equal to the ratio of distance traveled per unit of time.

    v(avg) = Δx(vector)/Δt​

    Notice that you may not need to use kinematics equations, as you are implicitly given the times for each velocity through the implications of the ratio km/h and the units km.

    Regarding the second question:
    Consider that speed is a scalar and not a vector.
     
  5. Nov 26, 2014 #4

    NascentOxygen

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    Staff: Mentor

    The speed calculation involves the actual distance the wheels travelled. So if a car headed 10 km E then returned along the same road to its starting point, its distance travelled would be 20 km. Divide this by total time to calculate the average speed.

    In contrast, velocity is a vector, and for average velocity you look at only where the vehicle started and where it ended up---determine the vector representing the difference between these two points, then divide by the total time of travel. So, for example, where the car returns to its starting point, the displacement is 0 km, making average velocity also 0 m/s.
     
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