In Motion! Rates of change. Rate of Change The word rate means with respect to time (i.e. your rate of pay is in $/hour, or $/month, or $/year. If you.

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Presentation transcript:

In Motion! Rates of change

Rate of Change The word rate means with respect to time (i.e. your rate of pay is in $/hour, or $/month, or $/year. If you slowly drain water out of a tank, the flow would be measured in litres/unit of time (seconds, or minutes or hours) Speed is a rate of change. It is how much distance you travel per unit of time (m/s, or km/h)

Speed vs. Velocity Speed is a scalar quantity. We calculate it by the equation v=d/Δt, or v = d/t, where d is the distance travelled, and t is the time it took to travel the distance. i.e. What was your speed if you travelled 1500 meters in 150 seconds: Given: d = 1500 m t = 150 s v = ? v = d/t v = 1500/150 v = 10. m/s

Velocity Velocity is given by where is the displacement. Velocity requires a direction. You must travel 200km/hr West for one hour to reach Brandon. To calculate velocity, you often have to first calculate the displacement using x f - x i. Your answer must include a direction.

Uniform Velocity Uniform velocity is a fancy way to say constant speed in the same direction (i.e. cruise control down the number 1 hwy due West). This means that with every second that passes, you cover the same amount of terrain in the same direction. You do not speed up, slow down, or change direction when you travel with a uniform velocity.

Examples A car travels 20 km E in a half hour. Calculatea. the car’s speed b. the car’s velocity. Given: d = 20 km t =.5 h v = ? v = d/t v = 20/.5 v = 40 km/h = 20 km,E/.5h = 40 km/h, E Speed is 40 km/h, velocity is 40 km/h, E

You can use this v=d/t equation to solve for d and t as well i.e. a car travels with a uniform velocity of 80 km/hr due North for 2 hours. Calculate displacement. Given: t = 2 hours

Average Speed Average Velocity Average speed = total distance/total time Average velocity = displacement/total time