The arrival time can be found by rearranging the average velocity formula: The pigeon's home is at position x 2, which is: If the average velocity of the pigeon is 20.0 m/s, at what time should the pigeon arrive back at its home?Īnswer: The problem is easiest to solve if the position of the cage is assigned to be x 1 = 0.0 m. At that time, the cage was 108.0 km from the pigeon's home. This means that the average velocity can also be stated as 33.33 m/s, toward Toronto.Ģ) A homing pigeon was released from its cage at 10:00 am.

The average velocity is -33.33 m/s, with the direction defined as above. The average velocity can be found using the formula: Using these conversions, the positions and times are: There are 1000 meters in 1 kilometer, and so 1 kilometer is: There are 60 minutes in an hour, and 60 seconds in a minute, and so 1 hour is: The question asks for the velocity to be stated in meters per second, so these positions and times must be converted. The travel time is given as a difference, so the start time is chosen to be t 1 = 0 hours. The start position x 1 = 220 km, and the end position x 2 = 100 km. Using this definition for direction, the resulting value of velocity will be negative. The average velocity formula describes the relationship between the length of your route and the time it takes to travel. We can now substitute these values in to get. We can use the quotient rule to find the derivative of the position function and then evaluate that at. If the location, Toronto, is chosen as x = 0, and the distance values are chosen to be positive, then the vehicle is moving in the negative x direction. The velocity is given as the derivative of the position function, or. In this case, the positions are expressed as distances away from a location. What is the velocity of the vehicle the boy is in, expressed in meters per second?Īnswer: The choice of direction is important when solving velocity problems. Exactly one hour later, he sees a sign that says Toronto is 100 km away. Average Velocity Formula (displacement over time) Questions:ġ) On a driving vacation, a boy sees a road sign that says Toronto is 220 km away.

Average velocity formula calculus