Physics “Motion in One Dimension”

Displacement and Velocity u motion - a constant change in position u distance - the result of motion in any direction u displacement - the result of motion in a particular direction(sign indicates direction) u scalar - a quantity having magnitude only u vector - a quantity having magnitude and direction

Speed or Velocity? u speed - the time rate of change in distance u velocity - the time rate of change in displacement u Speed is a scaler. Why? u Velocity is a vector. Why? u For now, we will use the terms speed and velocity without regard to direction.

Sample Problem u A runner runs 500m in 1.0 minute. What is the runners average speed in m/s? km/h? u v = Δ x /t = 500m/1m(1m/60s) = 8.3m/s u Devise a conversion factor that changes m/s to km/h. u 1m/1s(1km/1000m)(60s/1m)(60m/1h) = 18/5 u To change km/h to m/s multiply by 5/18.

Acceleration u acceleration - the time rate of change in velocity u a = (v f - v i ) / t u A car moving at 25m/s increases to 55m/s in 5 seconds. Find its rate of acceleration. u a = (55m/s - 25m/s)/5s = (30m/s)/5s = 6m/s 2 u What does negative acceleration indicate

Distance With Constant Acceleration u If an object is experiencing acceleration, the average velocity can be found by simply averaging the two velocities v i and v f. u v av = (v i + v f ) / 2 u The distance can then be calculated from this average velocity by using the simple equation for distance, Δx = vt. u Δx = [(v i + v f ) / 2] t

Sample Problem u A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find how far the car moves while stopping.

Velocity and Displacement with Constant Acceleration u If the constant acceleration is known, the equation rearranged to yield an equation for initial velocity. u Solve the equation for v f., a = (v f - v i )/t u If an object starts from rest, v i = 0. Given u Δx = [(v i + v f ) / 2] t and v f = v i + at, derive the equation for displacement.  Δx = v i t +  at 2

Sample Problem u A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8m/s 2 for 15s before takeoff. What is the speed at takeoff? How long must the runway be for the plane to be able to take off? u Assignment: Page 69, 26-29

Final Velocity After any Displacement u Using the equations for final velocity and displacement during constant acceleration, we can derive an equation for final velocity after any displacement. u Use: v f = v i + at and Δx = (v i + v f /2)t u Answer: v f 2 = v i 2 + 2a Δx

Sample Problem u A baby sitter pushing a stroller starts from rest and accelerates at a rate of 0.500m/s 2. What is the velocity of the stroller after it has traveled 4.75m? u Page 71, 30-33

Falling Objects u When gravity acts on an object, the object is accelerated at the rate of 9.8m/s 2, 980cm/s 2, or 32ft/s 2. u These numbers are constant and should be memorized. u Any time free fall is involved, a in an equation should be replaced with g, the acceleration due to gravity.

Sample Problem u A baseball is hit and remains in the air for 10 seconds. What is the maximum height of the ball? u Class Assignment: Find the height of the goal posts on the football field using a stopwatch and a baseball. u Page 74, 42-46

Experiment u You will roll a ball down an incline and measure the time required for it to roll 0-10cm, 0-20cm, etc up to 0-100cm. Make three trials and average each. u Record all average values in a data table. u Plot a graph of x vs t. u Analyze the graphs with regards to constant and varying slopes. u Write a ppoc for this experiment.

Plotting Graphs u 1. Identify the independent and dependent variables. u 2. Choose the appropriate range and plot the independent variable values on the x-axis and dependent on the y-axis. u 3. Decide if the origin is an appropriate point. u 4. Number and label the horizontal axis. u 5. Repeat steps 2-4 for the dependent variable. u 6. After plotting all points, draw the best fitting line through as many points as possible. u 7. Give the graph a title that best describes what it represents.