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Motion and Newton's Laws

# GED Science Practice Test: Motion And Acceleration

In physics, motion defined as the change in position of an object with respect to a frame of reference. A frame of reference is a place and time that you use for comparison.  For example, a car has motion because it changes it position with respect to an unmoving road beneath it.  The road beneath the car is the frame of reference. If the position of an object is not changing with the time with respect to a given frame of reference the object is said to be at rest, motionless, immobile, stationary, or to have constant position.

We can describe motion in a number of ways.  A common way to describe motion is through a rate, like velocity or acceleration.   However, other ways include displacement, direction, and time.  In terms of physics, there are two kinds of ways to measure motion.

Scalars are quantities that are described only by size, or magnitude, and do not have a direction. Commonly-used scalar quantities include:

• Distance: refers to “how much ground an object has covered” during its motion.
• Speed: refers to “how fast an object is moving.” Speed can be thought of as the rate at which an object covers distance.

Vectors are quantities that are described by both a magnitude and a direction. Commonly-used vector quantities include:

• Displacement: refers to “how far out of place an object is”; it is the object’s overall change in position.
• Velocity: refers to “the rate at which an object changes its position.” Imagine a person moving rapidly – one step forward and one step back – always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity. Because the person always returns to the original position, the motion would never result in a change in position. Since velocity is defined as the rate at which the position changes, this motion results in zero velocity.

Because velocity and displacement are vector quantities, they are direction-aware. This means that, when calculating the velocity or displacement of an object, one must keep track of the direction in which the object has moved or is moving. For example, you cannot say that an object has a velocity of 55 mi/hr; rather, you would have to describe an object’s velocity as being 55 mi/hr, east. This is an essential difference between speed and velocity, and between scalar quantities and vector quantities. Speed is a scalar quantity and does not keep track of direction; velocity is a vector quantity and is direction aware.

Let us examine the following diagram in order to distinguish between scalar and vector quantities:

If a person at point A traveled to the tree at point C and then to the house at point B, the person will have traveled 8 meters.  8 meters describes the distance the person traveled.  However, the change in position of the person o the bike is 4 meters; the person ended up 4 meters away from where she started.  In fact, because displacement is a vector quantity, we say that the person’s displacement was 4 meters to the North (we could be more specific about direction with degree measurements, but we are not worried with that degree of precision for this lesson).

Let’s consider the time it took this person to travel this path on her bicycle.  Suppose it took the person 4 seconds to bike this path.  We can calculate the person’s speed with the following formula:

So, the person’s speed would be 8 meters divided by 4 seconds, which equals 2 meters per second.  Speed describes the rate at which the distance was covered; two  meters were covered for each second the person traveled on her bike.

However, velocity, a vector quantity, is calculated using displacement, instead of distance:

So the velocity of the person on the bicycle is 4 meters (displacement) divided by 4 seconds, which equals 1 meter per second to the north.  Notice that velocity includes a direction, since displacement included a direction.

Sometimes in physics, it is necessary to add vectors together. You will see how this can be useful when you learn about forces later in this unit.  Adding vectors is a bit different from adding scalar values, because you have to factor in direction in addition to magnitude. Two vectors can be added together to determine the result (or resultant vector).  When the vectors you are trying to add together are in the same linear direction, can consider the resultant vector to almost be like moving places on a number line in math:

However, when the vectors are not in the same linear direction, you can use the triangle method of summing the vectors:

Acceleration is another vector quantity that describes a rate.  Acceleration is the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity over a period of time.  Thus, an object is accelerating if it is changing its speed and/or its direction.

It is important to note that acceleration is the rate of change of velocity; it does not mean that an object is moving fast.   A car traveling at constant rate of 80 mph hour has a high velocity, but has zero acceleration, since its speed its not changing.  Alternatively, acceleration does not necessarily mean that an object is speeding up.   Positive acceleration indicates “speeding up” with negative acceleration indicates “slowing down.”  Sometimes negative acceleration is called deceleration.  The vector (or direction) for acceleration indicates whether or not the car is speeding up relative to its direction, or slowing down relative to its direction.  The following shows changing velocity that represents acceleration, and changing velocity that represents negative acceleration, or deceleration.

Sometimes an object will experience constant acceleration, where the velocity changes by the same amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity. The following data tables depict motions of objects with a constant acceleration and a changing acceleration. Note that each table shows changing velocity, but that the velocity changes in different ways; the table on the left shows constant acceleration, while the table on the right shows changing acceleration:

The average acceleration (a) of any object over a given interval of time (t) can be calculated using the equation below, where the letter delta (Δ) means “change in”. So Δvelocity means “the change in velocity.” Vf = final velocity and Vi = initial or starting velocity.

Acceleration values are expressed in units of velocity/time. Typical acceleration units include the following:  miles/hour/second (mi/hr/s), kilometers/hour/second (km/hr/s), and meters per second squared (m/s2, sometimes expressed as m/s/s).  While these unit may seem confusing, consider the following problem:

A car accelerates from zero to 60 miles per hour in 4 seconds.  Calculate the car’s acceleration.

Using the formula, I calculate the change in velocity by taking the final velocity (vf) of 60 mi/hr and substract the initial velocity (vi) of 0 mi/hr.  The change in velocity is 60 mi/hr.  Then I divide the change in velocity by the time, which is 4 seconds.  So 60 divided by 4 is 15.  The complete answer with units is 15 mi/hr/s.  What this means it that for each second the car travels, it picks up an additional 15 mi/hr in speed.  So after one second, the car is going 15 mi/hr.  After another second, the car is going 30 mi/hr.  After yet another second, the car is going 45 mi/hr, and so on.

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