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Kinematics

 

Kinematic Equations

  1. V=Vo + at

  2. X= 1/2 (V + Vo ) t

  3. X= Vo t = 1/2at²

  4. V²= Vo ² + 2aX

Variable Definitions!!

V = Final Velocity (final velocity is the velocity at the end of a period of time.)

Vo = (Vnot) Initial Velocity (initial velocity is the velocity of a body or particle at the start of a period of time.)

a = acceleration (Acceleration is the rate of change of velocity with time.)

X= distance (An area that is covered. Measured in meters)

t= time (the amount of time it takes for the object to complete its motion. Measured in seconds.)

 

! Putting Kinematics to used!

Example problems:

1.)A truck accelerates from rest to 15 m/s in 4 seconds. Solve for the acceleration.

Step 1.) Choose one of the four equations that will best solve for acceleration. (V=Vo + at)

Step 2.) Fill in all the information in place of its corresponding variables.

15= 0+a4

Since the truck begins at rest, its initial velocity is zero. The final velocity is then the last recorded speed at which it was traveling when it reaches the stated time.

Step 3.) Simply solve the equation using the correct order of operation.

15= 4a a= 3.75 m/s²

    1. 4
  1. A car has an acceleration of -3 m/s². It was going 20 m/s. A ball rolls out in the road at a distance of 95 m. Can the car stop in time.

Step 1.) Choose one of the four equations that will best solve for acceleration. (V²=Vo ² +aX)

Step 2.) Fill in all the information in place of its corresponding variables.

0 = 20² + 2(-3X)

400 = -6X 400 = -6X X = 66.66m

-6 -6

*The distance it will take the car to stop is 66.66meters in length. If the ball was rolling a distance of 95 meters, then yes the car does in fact have time to stop.

 

3.)A car accelerates from 8 m/s to 12 m/s in 10 seconds. How far does it travel in this time?

Step 1.) Choose one of the four equations that will best solve for acceleration. (X = 1/2(V=Vo ) t )

Step 2.) Fill in all the information in place of its corresponding variables.

X = 1/2(12+8)10

1/2(20 10 = 10x10 = 100m

4.)Solve for the height of a building where a ball is dropped and falls for 3.4 sec.

Step 1.) Choose one of the four equations that will best solve for acceleration. (X= Vo t = 1/2at²)

Step 2.) Fill in all the information in place of its corresponding variables.

 

X =(0)t +1/2(9.8)(3.4)²

X = 1/2(113.288)

X = 56.6m

 

 

* Acceleration of objects that

are falling is always 9.8m/s²