Chapter 2 Motion in One Dimension 2-2 Acceleration

Any change in velocity is called acceleration. The sign (+ or -) of acceleration indicates its direction. Acceleration can be… speeding up slowing down turning

Uniform (Constant) Acceleration In Physics, we will generally assume that acceleration is constant. With this assumption we are free to use this equation: a = ∆v = vf - vi ∆t tf - ti SI Unit: m/s2

Acceleration has a sign! If the sign of the velocity and the sign of the acceleration is the same, the object speeds up. If the sign of the velocity and the sign of the acceleration are different, the object slows down.

Practice Problem A 747 airliner reaches its takeoff speed of 180 mph in 30 seconds. What is its average acceleration? Ans: 2.7 m/s2

Solution

Practice Problem (This is not in the handout) t v Describe the motion of this particle. It is moving in the +x direction at constant velocity. It is not accelerating.

Practice Problem (This is not in the handout) t v Describe the motion of this particle. It is stationary.

Practice Problem (This is not in the handout) t v Describe the motion of this particle. It starts from rest and accelerates in the +x direction. The acceleration is constant.

Graph: Velocity vs Time B t v a = Dv/Dt Dv Dt What physical feature of the graph gives the acceleration? The slope, because Dv/Dt is rise over run!

Practice Problem (back to the handout!) Determine the acceleration from the graph. Ans: 1.0 m/s2

solution

Position vs Time Graphs Particles moving with no acceleration (constant velocity) have graphs of position vs time with one slope. The velocity is not changing since the slope is constant. Position vs time graphs for particles moving with constant acceleration look parabolic. The instantaneous slope is changing. In this graph it is increasing, and the particle is speeding up.

Uniformly Accelerating Objects (This is not in the handout) You see the car move faster and faster. This is a form of acceleration. The position vs time graph for the accelerating car reflects the bigger and bigger Dx values. The velocity vs time graph reflects the increasing velocity.

Pick the constant velocity graph(s)… (This is not in the notes.) A t x C v B D

Draw Graphs for Stationary Particles (Back to the handout!) x t Position vs time v t Velocity vs time a t Acceleration vs time

Draw Graphs for Constant Non-zero Velocity x t Position vs time v t Velocity vs time a t Acceleration vs time

Draw Graphs for Constant Non-zero Acceleration x t Position vs time v t Velocity vs time a t Acceleration vs time

Kinematic Equations (pg 58) vf = vi + at Use this one when you aren’t worried about x. Δx = vit + ½ at2 Use this one when you aren’t worried about vf. vf2 = vi2 + 2a∆x Use this one when you aren’t worried about t. Δx = ½ (vi + vf)t Use this one when you aren’t worried about a.

Practice Problem You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and decelerate at 3.5 m/s2. How far do you travel before stopping? When you have traveled only half the stopping distance, what is your speed? How long does it take you to stop? Sketch approximate x-vs-t, v-vs-t, a-vs-t graphs for this situation.

Solution