Motion in one dimension Chapter 2 Motion in one dimension

One-Dimensional Motion with Constant Acceleration Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. The final velocity equals the initial velocity plus the acceleration x time vx = v0 + at v2x = v2x0 + 2ax(Δx) The final position equals the initial position plus the velocity multiplied by time plus one hals the acceleration multiplied by the time squared x = x0 + vx0(t) + ½ at2

One-Dimensional Motion with Constant Acceleration https://www.youtube.com/watch?v=H3Ragxvt-mU

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. Initial velocity Changing velocity Acceleration (constant) Positive velocity Positive acceleration

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. Initial velocity Constant velocity, positive Acceleration, constant, zero

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. Initial velocity Changing velocity Acceleration (negative), constant

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. Changing velocity Initial velocity Acceleration, negative Acceleration is not constant, decreasing acc. over time

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. Changing velocity Acceleration, positve Acceleration not constant

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. No initial velocity, accelerates at a constant rate during the A period No acceleration, constant velocity during the B period Negative acceleration during the C period At the end of the observation, the object is still moving

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. a = +1 m/s2

Velocity vs. Time Graph The shape of a velocity vs. time graph can yield valuable qualitative and quantitative information. a = +0.3 m/s2 a = +3 m/s2 a1 = +1.6 m/s2 a2 = -1.6 m/s2

Velocity vs. Time Graph The slopes of one graph can be graphed as well and so on…

Freely falling objects We usually disregard air resistance. A “freely falling object is moving under the influence of gravity alone. e.g. cannonball, arrow, something dropped, planetary motion, etc… Free-fall acceleration on Earth, g, -9.80 m/s2 Typical problems include: The impact speed of an object dropped from a known height Calculating the height of a fall

Freely falling objects To find the displacement of an object thrown straight up, y = y0 + v0t + ½ at2 You may need to calculate time to the highpoint first Keep in mind that, at the highpoint, vy = 0 vy = voy + at

Freely falling objects https://www.youtube.com/watch?v=c5spRGiakb0