K INEMATIC E QUATIONS. The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion.

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Presentation transcript:

K INEMATIC E QUATIONS

The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) Or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing.

d = 1/2 (v o + v f ) t a = (v f - v o ) / t d = v o t + 1/2 at 2 v f 2 = v o 2 + 2ad d – displacement t – Time v o – Initial velocity v f – Final velocity a – Acceleration

These four equations will be used to find unknown information about an object’s motion. There is a set strategy to follow when completing kinematic problems. The strategy involves the following steps: Construct an informative diagram of the physical situation. Identify and list the given information in variable form. Identify and list the unknown information in variable form. Identify and list the equation that will be used to determine unknown information from known information. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. Check your answer to insure that it is reasonable and mathematically correct.

Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s 2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Diagram:Given: v i = 0 m/s t = 4.10 s m/s a= 6.00 m/s 2 Find: d Which equation will you want to use??

K INEMATIC E QUATIONS AND F REE F ALL For objects experiencing free falling motion, we are still able to use the same kinematic equations but there are some specific concepts that apply: An object in free fall experiences an acceleration of 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. 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.

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 ( v f ) after traveling to the peak would be assigned a value of 0 m/s.

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.

Luke 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. Given: v i = 0.0 m/s d = m a = m/s 2 Find: t = ??

Rex throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Given: v i = 26.2 m/s v f = 0 m/s a = -9.8 m/s 2 Find: d??