A point against which position is measured

A physical measurement that contains directional information

A physical measurement that does not contain directional information

The time rate of change of an object’s velocity

The motion of an object when it is falling solely under the influence of gravity

The reference point allows you to determine whether or not position changes.

You are in a boat with your family and you see your friends on shore. You are waving to them as the boat is moving towards the shore line.

a. Who is in motion relative to you?

b. Who is motionless relative to you?

A. Your friends on the shore are in motion in relative to you because they are getting closer to you as the boat gets closer to the shoreline.

B. Your family is motionless relative to you. Their position relative to you does not change. They are

 therefore motionless with respect to you.

A. What is the formula for speed?

A. Equation for speed is: miles/distance

Example: a man is riding a bike for 20 miles in 2 hours. What is the speed he is riding his bike at?

20 miles

2 hours    =  10 miles per hour or 10mph

Again, we have the man riding a bike but this time he is riding his bike for 20 miles for 120 minutes and we want to know how many miles per hour he is riding his bike.

Now the measurements do not agree. What do you do?  

You must convert your measurements so they agree. So you must change minutes to hours.

120 minutes  x    1 hour

      1              60 minutes     = 2 hours

Now you can solve for speed:

20 miles

                 2 hours      = 10mph

What is the velocity of a motorcycle (in meters per second) if it travels 15 kilometers south in 20 minutes?

The problem wants velocity, which is speed and direction. To get speed, we will use Equation (9.1). Unfortunately, the problem tells us to give the answer in meters per second, but the distance is in kilometers and the time is in minutes. Thus, we need to do two conversions:

20 minutes  x 60 seconds

     1              1 minute         = 1200 seconds

15 kilometers   x   1000 meters

        1                 1 kilometer      = 15,000 meters

Now we can solve for speed:

15,000 meters

1200 seconds       =   12.5 meters per second

Not quite done, the answer wants a vector quantity so the answer is:

12.5 meters per second north

You are looking in a scientist’s lab notebook and find the following unlabeled measurements. In each case, determine what physical quantity the scientist was measuring.

a. 15.2 meters per second

b. 99 feet

c. 52 millimeters per hour to the west

d. 10.5 yards per minute²

 north

A. This measurement has a distance unit divided by a time unit. That’s speed or velocity.

Since no direction is given, this is speed.

B. The unit of feet by itself measures distance.

C. This measurement has a distance unit divided by a time unit. That’s speed or velocity. Since a direction is given, this is velocity.

D. This measurement has a distance unit divided by a time unit squared. That’s acceleration. The direction is necessary because acceleration is a vector quantity.

How do we determine relative velocity in this problem?

A police car is chasing a criminal. The police car is traveling at 85 mph east and the criminal is traveling at 86 mph east?

                   85 mph east -->        86 mph east -->

[image]   [image]

You minus the speed of the criminal car from the police car from the criminal car which 86mph - 85mph = 1mph.

Since the criminal car is traveling faster than the policae car, the criminal is pulling away. Thus, the relative velocity is:

1.0 mph away from each other.

What is the acceleration of an object that moves with a constant velocity?

Since the velocity is not changing, the acceleration is zero.

What is the equation for acceleration?

final velocity - initial velocity

      time     

= acceleration     

Solve for acceleration:

A skateboarder skates with velocity of 4 meters per second north. If the skateboarder comes to a complete stop in 2 seconds, what was his acceleration?

0 meters/second - 4 meters/second             

                  2 seconds                      = 

-4 meters/seconds

      2 seconds           =   -2 meters/second² north

A speedboat goes from 0 to 70 miles per hour north in 9 seconds. What is the boat’s acceleration?

Hint: you have measurements that do not agree and you need to convert before you solve for acceleration

Convert seconds to hours first:

9 seconds    x     1 hour

      1             3600 seconds   =  0.0025 hour

Now solve for acceleration:

70 miles/hour - 0 miles/hour

               0.0025 hour                 =   

Final answer: 28,000 miles/hour² north

 You are standing over a cliff and are holding a rock and a ball in each hand. You throws the ball down towards the river as hard as he can and at the same time simply drops the rock. After both have left the person’s hand, does one have a greater acceleration? If so, which one?

Neither has greater acceleration. Both objects are falling near the surface of the earth; thus, they are each in free fall. That means they both have equal acceleration. The ball was given more

initial velocity, so it will travel faster. The acceleration on both is the same, however.

Why does a dropped piece of paper hit the ground later than a baseball dropped at the same time?

The paper is more affected by air resistance than the baseball. This is the same situation as Experiment 9.2.

You decide to climb up an oak tree. To measure how high you have climbed, you drop a rock and time its fall. It takes 1.2 seconds for the rock to hit the ground. How many feet have you climbed?

Hint: Use equation 9.3 and don't forget that acceleration for gravity in english units in 32 feet/second²

distance = 0.5 x (acceleration) x (time)²

With equation 9.3 from your book, you can use this equation to solve the problem:

0.5 x 32feet/second²  x (1.2)^{2 =}

0.5 x 32 feet/second²  x 1.2 x 1.2 =

23.04 feet