Displacement, Velocity & Acceleration Honors/AP Physics Mr. Velazquez Rm. 254 1
Velocity vs. Speed Speed and velocity can both be defined as a change in position or displacement over time. However, speed is a scalar quantity (a magnitude only, with no direction), while velocity is a vector quantity (a magnitude with direction). Because of this important distinction, we should also recognize the difference between distance and displacement. Distance is a scalar quantity that describes how far the object travelled, no matter where it ends up Displacement is a vector quantity describes how far the object is from the starting point, and can be defined as the final position minus the initial position. average speed = distance traveled time elapsed average velocity = displacement time elapsed 2
Position vs. Time Sometimes a graph can be a great way to represent the motion of one or more objects. In the example below, a blue car begins moving at a constant velocity at a position a little ahead of the starting point. Soon, a red car surpasses the blue car. The graph plots their position over time. A reference point is important here. In this example, we are using position 0.0 m as our reference point for position. The slope of a position vs. time graph represents the object s velocity. 3
Position vs. Time Velocity is constant between t = 0 and t = 5 Velocity is NOT constant between t = 0 and t = 5 4
Instantaneous Velocity Motion is very rarely uniform. Even though the average velocity may be true for a particular span of time, the object probably traveled faster or slower than that velocity at certain points. Because of this, we refer to a concept known as instantaneous velocity, which we define as the object s actual velocity at a certain exact moment in time. Another way of expressing the instantaneous velocity is the average velocity over a very short period of time (infinitely small) v = x t = x 2 x 1 x = lim t 2 t 1 t 0 t 5
Footer Text Practice: Average Velocity A runner s position on the track changes during a 3.00-second time interval from x 1 = 50.0 m to x 2 = 30.5 m. What is the runner s average velocity? v = x t = x 2 x 1 t 2 t 1 v = 30.5 m 50.0 m 3.00 s 0.00 s = 19.5 m 3.00 s v = 6. 50 m/s 6
Acceleration An object is said to experience acceleration when it s velocity is changing. Note: An object that is slowing down is still said to have acceleration it s merely a negative acceleration. Average acceleration is calculated by dividing the change in velocity (a vector) by the change in time (a scalar), which makes it a vector quantity. We can also discuss an object s instantaneous acceleration the same way we would define average velocity. a = change in velocity time elapsed = v 2 v 1 = v t 2 t 1 t a = lim t 0 v t 7
Practice: Average Acceleration A car accelerates along a straight road from rest to 75 km/hr in a period of 5.0 s. What is the magnitude of the average acceleration? a = v t = v 2 v 1 t 2 t 1 a = km 75 hr 0 km hr 5.0 s 0 s v = 15 km/hr s = 75 m s 5.0 s 8
Velocity vs. Time Describe the motion of the object in this graph. 9
Footer Text Deceleration A bicycle moving at 22.0 m/s applies its brakes and begins slowing down at a constant rate of 4.50 m/s 2. How long will it take for the bike to come to a complete stop? a = v t = v 2 v 1 t Rearranging this equation, we can solve for t: t = v 2 v 1 a t = 0 m s 22.0 m s 4.50 m = 22.0 m s s 2 4.50 m s 2 t = 4. 89 s 10
Footer Text Classwork/Exit Ticket 1. Create a position vs. time graph for an object that starts at x=0, moves forward at 2 m/s for 4 seconds, rests for 2 seconds, then moves backward at 3 m/s for 5 seconds. 2. Calculate the average velocities of an object that moves from position x=0 m to x=30 m in (a) 5 seconds, (b) 10 seconds, and (c) 20 seconds. 3. Calculate the average acceleration of a vehicle that goes from 0 m/s to 80 m/s in (a) 6 seconds, (b) 12 seconds, and (c) 15 seconds. 11