Download • vf • If vi = 0, vf

Acceleration • Time rate of change of velocity; A vector; Symbol
a and units of m/s/s usually 2 shortened to m/s • Acceleration can be negative • Average acceleration = change in velocity / elapsed time for the change • Galileo first to understand acceleration 1st Constant Acceleration Equation • If acceleration is constant, instantaneous acceleration always equals avg acceleration • Use definitions of avg velocity and accel to calculate final velocity or distance • Since a = (vf ­ vi)/t , then vf = vi + at • If motion starts from rest, vi = 0 , then vf = at • Use when distance not given or asked for 2nd Constant Acceleration Equation • vavg = (vf + vi)/2 ; but also vavg = d/t ; so (vf + vi)/2 = d/t • Now using our first equation for vf we can get (vi + vi + at)/2 = d/t • Solving for d: d = vit + 1/2 at 2 • If vi = 0, d = 1/2 at 2 • Use when final speed not given or asked for 3rd Constant Acceleration Equation • Solve 1st equation for t and substitute into 2nd equation, expand squared quantity and combine terms. • Get 2ad = vf 2 ­ vi 2 ; solve for vf 2 • vf 2 = vi 2 + 2ad • If vi = 0, vf 2 = 2ad • Use when time is not given or asked for Graphing Motion: d vs t • Plot time as independent variable • On position vs time graph, slope at any value of t gives instantaneous velocity • If graph is linear, slope and v are constant • If graph is curved, slope and v are found by drawing tangent line to curve and finding its slope Graphing Motion: v vs t • Slope of v vs t graph gives acceleration • If graph is linear, acceleration is constant • If graph is curved, instantaneous acceleration is found using slope of tangent line at any point Velocity vs Time Graphs: Finding Displacement
• Displacement can be found from velocity graph by finding the area between the graph • • • and the time axis This process is called integration To integrate graphically, divide the area bounded by the graph line (curve), the horizontal axis and the initial and final times into geometric sections (squares, rectangles, triangles, trapezoids) and find the area Area above the time axis is positive displacement, below the time axis is negative displacement Free Fall • One common situation for constant acceleration is free fall • Force of gravity causes falling bodies to accelerate • Force varies slightly from place to place but average acceleration is 9.80 m/s 2 designated by symbol g • Can use all constant acceleration equations for free fall • Usually are written with symbol g in place of a in equations and y in place of d or x • Motion is vertical so upward and downward motion must have opposite signs • If air drag is ignored, all objects fall at the same rate • Air resistance slows rate of fall • If upward drag force equals downward force of gravity, terminal velocity is reached and acceleration is zero Kinematics Equations • Horizontal Motion Vertical Motion v f = v i + a Dt v f = v i + g Dt D x = v i Dt + 1 2 a ( Dt ) 2 D y = v i Dt + 1 2 g ( Dt ) 2 v 2 f = v i 2 + 2 a Dx v 2f = v i 2 + 2 g Dy