## Physics 221, January 19

Key Concepts: • Scalar Quantities and Vector Quantities • Position, Distance, Displacement • Average Speed, Average Velocity • Instantaneous Speed, Instantaneous Velocity • Average Acceleration, Instantaneous Acceleration

## Physics: the key word is change !

Matter interacts and the interactions change the physical state of matter.

The laws of physics predict when and how the physical state of matter changes.

Mechanics : Change < -- > Motion The laws of mechanics predict when and how things move.

We have to agree on a way to describe motion.

Vector quantities with magnitude and direction are used in describing motion: Position: r = ai + bj + ck Displacement: Average velocity: d = (x 2 - x 1 )i + (y 2 - y 1 )j + (z 2 -z v = d/∆t. Instantaneous velocity: 1 )k Let ∆t  0.

Average acceleration: a = ∆v/∆t.

Instantaneous acceleration: Let ∆t  0.

Scalar quantity with only magnitude are also used in describing motion: Examples: distance, average speed, instantaneous speed

Extra Credit:

Four different mice (labeled A, B, C, and D) ran the triangular maze shown below. They started in the lower left corner and followed the paths of the arrows. The times they took are shown below each figure, (i) Which mouse had the greatest average speed?

(ii) Which mouse had the greatest average velocity?

## 1.

2.

3.

4.

(i) D, (ii) C (i) B, (ii) A (i) A, (ii) D (i) B, (ii) C

0% 1 0% 2 0% 3 0% 30 4

## Motion in 1 dimension

If an object is restricted to move in one dimension, for exampe along the x axis, we can specify the vector quantities position, displacement, velocity, and acceleration by a signed number with units . The sign of the number than specifies the direction.

In one dimension, if the x-component of a vector is positive, the vector is pointing in the positive x-direction, and if the x-component of a vector is negative, the vector is pointing in the negative x-direction.

We can represent one-dimensional motion using a

position versus time graph

or a

velocity versus time graph

.

The

position versus time

graph represents the motion of an object moving in a straight line. Find the objects instantaneous velocity at (a) t=0.5s, (b) t=2.0s, (c) t=4.0s.

1.

2.

3.

4.

5.

2 m/s, (b) 5 m/s, (c) 6 m/s 2 m/s, (b) 8 m/s, (c) 10 m/s 0 m/s, (b) 8/3 m/s, (c) 2 m/s 0 m/s, (b) 3 m/s, (c) 1 m/s 0 m/s, (b) 3/2 m/s, (c) 1/2 m/s

30 0% 1 0% 2 0% 3 0% 4 0% 5

The

position versus time

graph represents the motion of an object moving in a straight line. Find the average velocity of the object between (a) A and C, (b) A and D, (c) B and D.

1.

2.

3.

4.

5.

30

2 m/s, (b) 8/5 m/s, (c) 2 m/s 8/3 m/s, (b) 2 m/s, (c) 5/2 m/s 4 m/s, (b) 5 m/s, (c) 6 m/s 8 m/s, (b) 10 m/s, (c) 10 m/s 5 m/s, (b) 6 m/s, (c) 6 m/s

0% 1 0% 2 0% 3 0% 4 0% 5

The

position versus time

graph represents the motion of an object moving in a straight line. Is the magnitude of the average velocity equal to the average speed between A and D?

1.

2.

Yes No

30 0% 1 0% 2

The

position versus time

graph represents the motion of an object moving along a straight line. The velocity of the object is always positive.

1.

2.

True False

30 0% 1 0% 2

The

position versus time

graph represents the motion of an object moving along a straight line. What is the instantaneous velocity of the object at t = 14 s?

1.

2.

3.

4.

5.

30

-(1/15) m/s -(5/3) m/s 0.067 m/s (1/3) m/s -(2/3) m/s

0% 1 0% 2 0% 3 0% 4 0% 5

A friend is casually talking with you about physics concepts and brings up the following claim. “They say that average speed for a trip is total distance divided by total time, which is true. Then they say that if the trip consists of a person traveling at two different speeds for two different times then you can get the average speed by just finding the average speeds for the two parts of the trip and then take their average.” Is their claim true or false? What is your opinion?

## 1. True 2. False

30 0% 1 0% 2

The

velocity versus time

graph to the right represents the motion of an object moving in one dimension along the x-axis. The velocity of the object is always positive.

1. True 2. False

30 0% 1 0% 2

Extra Credit:

The

velocity versus time

graph to the right represents the motion of an object moving in one dimension. What is the object's average acceleration between t = 0 and t = 6s?

1. -3 m/s 2 2. 1.5 m/s 2 3. -0.83 m/s 2 4. 0.67 m/s 2 5. 0.5 m/s 2

30 0% 1 0% 2 0% 3 0% 4 0% 5

The positions of two blocks at successive 0.20-second time intervals are represented by the numbered squares in the figure below. The blocks are moving towards the right. The accelerations of the blocks are related as follows : 3.

4.

5.

1.

2.

The acceleration of a is greater than the acceleration of b.

The acceleration of a equals the acceleration of b. Both accelerations are greater than zero. The acceleration of b is greater than the acceleration of a.

The acceleration of a equals the acceleration of b. Both accelerations are zero.

Not enough information is given to answer the question.

30 0% 1 0% 2 0% 3 0% 4 0% 5

Let the x-axis of your coordinate system point along a drag strip. A drag racer starts from rest and accelerates to a speed of 76.5 m/s in 8.5 seconds. What is the acceleration of the car? 1. 2.1 m/s 2 2. 68 m/s 2 3. 9 m/s 2 4. 650 m/s 2 5. 76.5 m/s 2

0% 1 0% 2 0% 3 0% 4 0% 5 30

Extra Credit: A 50-g superball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high speed camera records this event. If the ball is in contact with the wall for 3.5 10 -3 s, what is the magnitude of the average acceleration during this time interval?

1. 13429 m/s 2 2. 857 m/s 2 3. 47 m/s 2 4. 3 m/s 2 5. 0.01 m/s 2

30 0% 1 0% 2 0% 3 0% 4 0% 5