Physics Classroom: #2 Free Fall & Kinematics

What does the area in a velocity vs. time graph represent?

the area between the line and the time axis is equal to the displacement of the object. The displacement of the object can also be determined using the velocity-time graph. The area between the line on the graph and the time-axis is representative of the displacement; this area assumes the shape of a trapezoid.

How do you know which kinematic equation to choose when doing a kinematic calculation?

you will always choose the equation that contains the three known and the one unknown variable

What are two important motion characteristics that are true of free-falling objects?

•Free-falling objects do not encounter air resistance. •All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (approximated as 10 m/s/s)

Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

1. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. 2. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity.

What are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion?

1.An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. 2.If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. 3.If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. 4.If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height

What are the steps used to solve Kinematic problems?

1.Construct an informative diagram of the physical situation. 2.Identify and list the given information in variable form. 3.Identify and list the unknown information in variable form. 4.Identify and list the equation that will be used to determine unknown information from known information. 5.Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6.Check your answer to insure that it is reasonable and mathematically correct.

Acceleration of Gravity

A free-falling object has an acceleration of 10 m/s/s, downward (on Earth). This numerical value for the acceleration is known as the acceleration of gravity

Continuation of Question Before: Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.

An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below.

What is Kinematics?

Equations to describe and represent the motion of objects are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known.

True or False: Doesn't a more massive object accelerate at a greater rate than a less massive object?

FALSE That is, absolutely not if we are considering the specific type of falling motion known as free-fall. Free-fall is the motion of objects that move under the sole influence of gravity; free-falling objects do not encounter air resistance. More massive objects will only fall faster if there is an appreciable amount of air resistance present. All objects free fall at the same rate of acceleration, regardless of their mass.

Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period

Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s Always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d

True or False: Free falling objects are in a state of acceleration

TRUE They are accelerating at a rate of 9.8 m/s/s. (10 m/s/s) This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. If dropped from a position of rest, the object will be traveling 9.8 m/s (approximately 10 m/s) at the end of the first second, 19.6 m/s (approximately 20 m/s) at the end of the second second, 29.4 m/s (approximately 30 m/s) at the end of the third second, etc

What does the slope represent in a velocity vs time graph?

The slope of the line on a velocity-time graph is equal to the acceleration of the object. The slope of the line can be computed using the rise over run ratio. Between 5 and 10 seconds, the line rises from 5 m/s to 15 m/s and runs from 5 s to 10 s. This is a total rise of +10 m/s and a total run of 5 s. Thus, the slope (rise/run ratio) is (10 m/s)/(5 s) = 2 m/s2. Using the velocity-time graph, the acceleration of the object is determined to be 2 m/s2 during the last five seconds of the object's motion

Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.)

The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. Initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). Acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below.

The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by?

The use of a formula; the distance fallen after a time of t seconds is given by the formula. d = 0.5 * g * t2 (dropped from rest)

Continuation to sample problem: Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.)

There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it

What is the Velocity of a free falling object?

Velocity=gravity*time

What does a curved line on a position versus time graph signify for a free falling object?

a curved line on a position versus time graph signifies an accelerated motion Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. the slope of any position vs. time graph is the velocity of the object

Free Fall

an object that is falling under the sole influence of gravity Any object that is being acted upon only by the force of gravity is said to be in a state of free fall

What are the quantities used for Kinematics equations:

displacement (and distance) velocity (and speed), acceleration time

Calculate the distance for a (fallen) a free-falling object after one and two seconds

distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula. d = 0.5 * g * t2