Title: PH 201
1PH 201
- Dr. Cecilia Vogel
- Lecture 2
2REVIEW
- Motion in 1-D
- position
- displacement
- average velocity
- Special case
- Constant velocity
OUTLINE
- Motion in 1-D
- velocity and speed
- acceleration
- velocity and acceleration from graphs
3Summary
- Positive velocity
- Moving forward
- Value of position, x, increasing
- Slope of x vs. t is positive
- Negative velocity
- Moving backward
- Value of position, x, decreasing
- Slope of x vs. t is negative
- Zero velocity
- Stopped (maybe just for an instant)
- Occurs any time motion changes direction
- x vs. t graph is horizontal (maybe just for an
instant)
4Average Speed
- Average speed is the distance traveled divided by
the time interval.
- Compare to
- Average velocity is displacement divided by time
interval - Small wording difference, big difference in
results
Ex Object goes 5 cm in the negative direction
then two cm in the positive direction, all in one
second. vave -3 cm/s, save7 cm/s
Ex Object goes 5 cm in the negative direction in
one second. vave -5 cm/s, save5 cm/s
5Ave Speed Example
- Example
- Sharrona drives to her friends house along a
straight road at a constant 35 mph. She forgot
something, so returns home, traveling only 25
mph. - Find her average velocity and average speed.
- Problem-solving hints.
6Average Velocity on a Graph
- On a graph of position vs. time, average velocity
is the slope of a line connecting two points on
the graph.
7Velocity
Average velocity, given by slope of straight
line, doesnt describe everything that happens
during the time interval. (Instantaneous)
velocity describes what happens at a given
instant at a single point on the graph.
8Instantaneous Velocity
If you take a smaller time interval, you more
accurately reflect whats happening at that
instant.
9Velocity on Graph
- On a graph of position vs. time, (instantaneous)
velocity is the slope of a line tangent to the
curve at that instant.
10Instantaneous Speed
- Instantaneous speed is just the magnitude of the
instantaneous velocity. - Always positive.
- Note it is also the limit as Dt approaches zero
of the average speed. - As time interval goes to zero, theres no time to
change direction, so speed v
11Acceleration
- Average acceleration is
- Change in velocity over the time interval
- Objects acceleration is positive if
- vf gt vi
- velocity is increasing
- Remember that from -50 to -40 is an increase
- Speed NOT necessarily increasing!!
12Direction of Acceleration
- Three ways to find acceleration direction
- Is velocity (not speed!) increasing?
- if so, accel is
- dont forget -10 gt -50
- What direction do you feel tossed when you
accelerate that way? - imagine a car
- acceleration is OPPOSITE that
- What way would you have to push/pull to cause
that acceleration? - acceleration is in that direction
13Examples Way 1
- Velocity positive, speed increasing
- ex vi 30 mph, vf 60 mph
- velocity is increasing, a is _____
- Velocity positive, speed decreasing
- ex vi 30 mph, vf 20 mph
- velocity is decreasing, a is __-___
14Way 1, contd
- Velocity negative, speed increasing
- ex vi -30 mph, vf -60 mph
- velocity is decreasing, so a is _-__
- (speeding up, but negative accel!!!)
- Velocity negative, speed decreasing
- ex vi -30 mph, vf -20 mph
- velocity is __creasing, so a is __
15Way 2
- Your body is an accelerometer, you feel pushed
opposite the acceleration. - Velocity positive, speeding up
- feel pushed back
- opposite that, a is back or -
- Velocity positive, slowing down
- feel pushed _____
- opposite that, a is ____
16Way 2 contd
- Velocity negative, speeding up
- feel pushed forward
- opposite that, a is back or -
- Velocity negative, slowing down
- feel pushed ___
- opposite that, a is ___
17Sign of Acceleration
- Acceleration requires a force. How would you
have to push something to change its velocity? - Objects velocity is positive, if you want it to
speed up - must push forward,
- Push forward -gt a is forward or
- Objects velocity is positive, if you want it to
slow down - must push backward,
- push back -gt a is ___
18Sign of Acceleration
- Objects velocity is negative, if you want it to
slow down - push forward,
- so a is forward or
- Objects velocity is negative, if you want it to
speed up - push backward,
- so a is ___
19Acceleration on a Graph
- On a graph of velocity vs time, acceleration is
- However, on a graph of position vs. t,
- velocity is the slope,
- what is accel?
20Acceleration on a Graph
- In this region, v (slope) is decreasing
- Acceleration, then, is negative
21Acceleration on a Graph
- In this region, v (slope) is
-
- Acceleration, then, is
22Acceleration on a Graph
- In this whole region, slope is decreasing, the
curve is concave down - Acceleration, then, is negative
- Generally concave down is negative accel
23Acceleration on a Graph
- In this region of time, slope is increasing, the
curve is concave up - Acceleration, then, is positive
- Generally concave up is positive accel
24Summary
- Positive acceleration
- Moving forward and
- Or moving backward and
- Or stopped and starting forward
- _______ curvature on x vs t graph U
- Negative acceleration
- Moving backward and
- Or moving forward and
- Or stopped and starting backward
- ________ curvature on x vs t graph n