http://astro.temple.edu/~elenab/

Describing Motion:Kinematics in one dimension

Kinematics is a part of mechanics, which is the description of how objects move.

Translational

motion

Reference Frame

Speed

Speed is a measure of how fast object moves, measured by a unit of distance divided by a unit of time.

Instantaneous Speed

Average speed doesn’t indicate the different speeds that may have taken place during shorter time intervals.

Average Speed

average speed = total distance traveled/ time elapsed

Total distance traveled = average speed X time

1. What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s?

2. If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km.

(a) how far would it travel if it moved at this rate for 4 h?

(b) for 10 h?

3. In addition to speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one half hour later, what has been your average speed?

4. Would it be possible to attain the average speed in previous example and never go faster than 80 km/h?

Velocity

When we describe speed and the direction of motion, we are specifying velocity

Instantaneous Velocity

1. With what two physical values is the race-car driver concerned? Speed or velocity?

2. The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

3. During certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed or a constant velocity?

1. How might you estimate your speed if the speedometer in your car is broken?

2. Which of the following can be used to measure an average speed: stopwatch, odometer, or speedometer? An instantaneous speed?

Acceleration

We can change the velocity of something by changing its speed; by changing its direction or by changing its speed and its direction.

Acceleration

average acceleration = change of velocity/time elapsed

Acceleration tells us how fast the velocity changes, whereas velocity tells us how fast the position changes.

Motion at Constant Acceleration

Acceleration is a rate of change , or change per second of velocity.

v= at

1. Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 s, or a skateboard that goes from 0 to 5 km/h in 1 sec?

2. What is the acceleration of a race car that whizzes past you at a constant velocity 400 km/h?

Falling Objects

Acceleration on Galileo Inclined Planes

Galileo found greater accelerations for steeper inclines. The ball attains max acceleration when the incline is tipped vertically.

-a ball rolling down an inclined plane is moving with constant acceleration

- greater accelerations for steeper planes, max acceleration when incline is tipped vertically

- regardless of weight and size, when air resistance is small enough to be neglected, all objects fall with the same unchanging acceleration.

We call this acceleration the acceleration due to gravity on the Earth, and we give it the symbol g.

g = 9.80 m/ s2 ~ 10 m/ s2

How Far?

With his inclined planes Galileo found that the distance a uniformly accelerating object travels is proportional to the square of the time

Distance = acceleration x time x time /2.

It is common observation that many objects fall with unequal accelerations: a leaf, a feather or a sheet of paper may come to the ground slowly. Why?

At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration

A cat steps off a ledge and drops to the ground in ½ second.

(a) What is its speed on striking the ground?

(b) What is its average speed during the ½ second?

(c) What is the height of this ledge?

1. Which of the following (if any) could not be considered an “accelerator” in an automobile: gas pedal, brake pedal, steering wheel?

2. A sports car accelerates from 65 mph to 75 mph in 2 seconds while a minivan accelerates from 20 mph to 35 mph in 2 seconds. Which one has the larger acceleration?

3. You are standing on a high cliff above the ocean. You drop a pebble, and it strikes the water 4 seconds later. Ignoring the effects of air resistance, how fast was the pebble traveling just before striking the water? What is the height of the cliff?

Summary of Terms

Speed : How fast something moves. The distance traveled per unit time

Velocity: The speed of an object and specification of its direction of motion

Acceleration: The rate at which velocity changes with time; the change in velocity may be in magnitude or direction or both.

Free fall : Motion under the influence of gravity only.

Summary of Formulas

Speed = distance/time

Average speed = total distance covered/time interval

Acceleration = change of velocity/time interval

Acceleration (along a straight line) = change in speed/time interval

Velocity acquired in free fall, from rest: v=gt

Distance fallen in free fall, from rest: d = gt2/2