AP Physics With Hansenator - Kinematics

Kinematics

Kinematics is defined to be "the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion". Motion can be described a couple of ways, kinematics is probably one of the simplest because it only involves four equations!

---

The Equations and Variables

• s and d - distance
• v and r - final velocity or rate (speed)
• a - acceleration (changing speed)
• t - time
• o - initial (Ex. - initial distance from reference point)

---

The Motion of a Projectile

The motion of a projectile is a parabola. The reason is proven with calculus very easily, believe it or not. Most people don't know that a projectile has two speeds, not one! A speed in the x-direction and a speed in the y-direction. The reason is that gravity is an acceleration, so it pulls things towards the ground. The speed parallel to the ground Does Not Change. No matter what height you drop an object from it will always hit the ground at the same time, if you neglect air resistance. Here is a visual of these two speeds, or velocities, on a thrown object:

If angles are involved you find the two speeds with these equations:

• This is the symbol for the angle, theta:
• Remember vx is constant and vy changes because gravity pulls it down, so at the top it's motion vy = 0.

---

Examples

1. A car accelerates uniformly from a stop to 15 m/s in 3 seconds. What is the acceleration?
   "from a stop" means initial velocity is 0 m/s.
   15 m/s is our final velocity.
   
   
   
2. A car accelerates uniformly from a stop to 15 m/s in 3 seconds. How far did it go?
   
   
   
3. A ball is dropped from a height of 120 meters. How long did it take to hit the ground? Remember: the number for gravity is -9.8 meters per second squared.
   "dropped" means initial velocity is 0 m/s.
   
   
   
4. A ball is dropped from a height of 120 meters. How fast was it moving when it hit the ground?
   
   
   
5. A bullet is fired straight upwards with an initial velocity of 150 m/s. How high did it go? Hint: When the bullet reaches the top, how fast is it moving?
   
   
   
6. A golf ball is hit with a velocity of 25 m/s at an angle of 40 degrees. How long does it take to hit the ground? How far did it go horizontally?
   First, you need to find the two speeds of the ball. Next, to figure out how long it takes to get to the ground, use the s equation. Finally, to figure out how far it went you use the non-acceleration equation since velocity in the x-direction does not change.
   

---

Thank you for your support Steemers! Teach this to your kids! Ages 12+! It's hard,
but once you learn it it's not bad at all!