Velocity time graphs

Goals for today Discuss V-T graphs Homework In the books p 338-339 proms 2-7, 10-11, 14-16, 22-28 -- Graph handout Test for honors is Wednesday CP is Thursday

Differences between V-t graphs and P-T graphs The vertical #’s tell how fast, not location V-t does not indicate start position Direction is indicated by position on graph, not slope Acceleration is indicated differently on each type of graph

Horizontal lines on a V-T graph Velocity (m/s) Time (s)

Using the motion detector Can you mimic the graph Using the motion detector

Tilted lines on V-T graphs V (m/s) T (m/s)

What do tilted lines mean on a V-T graph? The object is changing its velocity Acceleration How it accelerates is determined by Location of graph (Above, Below x-axis) Type of tilt

Acceleration is… A change in the velocity of the object Tilted lines on a V-T graph indicate acceleration Acceleration can be calculated by finding the slope value of these lines

Tilted lines on V-T graphs V (m/s) T (m/s)

What kind of motion is indicated on this graph? V (m/s) T (s)

What would curves mean on a V-T graph Curves would indicate non-constant acceleration Think roller coaster rides, when you get pushed against the harness or back into the seat The ‘Jerk’

Identify motion for each part of the V-T graph V (m/s) T (m/s)

Identify motion for each part of the V-T graph V (m/s) T (m/s)

Create a V-t graph that… Section 1: Shows constant motion of (-3) m/s for 5 seconds. Section 2: Shows constant acceleration (slowing down in the negative direction) Section 3: Shows no movement for 5 seconds Section 4: Shows constant acceleration (speeding up in the positive direction)

Answer

Homework For all graphs: Find the direction Constant Velocity or Non-Constant Velocity Fast, Average or Slow Faster, Slower (Change in Velocity)

Finding overall displacement from V-T graph How far does an object travel if it goes 3 m/s for 10 seconds? V 3 t 10

Acceleration Anytime the velocity of an object changes, the object accelerates Getting Faster Getting Slower If the motion of object changes direction going the same speed

Velocity changes if… Speeding up Slowing down

Velocity changes if… The direction of the motion changes, but the speed does not This type of acceleration is call centripetal acceleration

Equation for average acceleration a = (vf - vi) / t vf = final velocity vi = initial velocity t = elapsed time a = acceleration

Ex #1 A flowerpot falls off a second story windowsill. The flowerpot start from rest and hits the sidewalk 1.5 s later with a velocity of 14.7m/s. Find the average acceleration.

What information is given? Identify the information. Is the time 14.7 m/s is the final velocity Starts from rest Means that the initial velocity is zero (0) “at rest” always means that vi = o

Answer #1 a = (14.7 – 0) / 1.5 = 9.8 What are the units? (14.7 m/s – 0 m/s) 1.5 s = (m/s) / s m / s2

Ex #2 While driving at an average velocity of 15.6 m/s down the road, a driver slams on brakes to avoid hitting a squirrel. The car stops completely in 4.2 seconds. What is the acceleration of the car?

What you want to solve for Givens 15.6 m/s = vi 4.2 s = t 0 = vf What you want to solve for acceleration

Solution a = (0 – 15.6) / 4.2 = (-3.7) m/s2

Questions on homework in book Pg 324 Pg 328

Mr. Baker’s Monster problem On a dark and scary night, Mr. Baker was walking down the street at 5.234 m/s. He heard a horrible sound of hundreds of shuffling feet behind him and increased his speed to a new 78.985 m/s. What was the amount of time (in minutes) needed to increase his speed, if his rate of acceleration was 1.9 m/s2 ?

Answer Given: vi = 5.234 m/s a = 1.9 m/s2 vf = 78.985 m/s Want: time (in minutes) a = (vf – vi) / t 1.9 = (78.985 -5.234) / t