Kinematics

Topic Overview Kinematics is used to analyze the motion of an object. We use terms such as displacement, distance, velocity, speed, acceleration, and time to describe the movement of objects.

Topic Overview Distance (m): The total meters covered by an object (odometer) Displacement (m): The difference between the start and end points.

Topic Overview Velocity (m/s): How fast the car is moving is a (+) and (–) indicate direction Acceleration (m/s 2 ) Acceleration is a change in velocity If an object is accelerating, it is either speeding up or slowing down

Some objects have constant velocity This means that acceleration = 0 The equation for constant velocity is: x = vt If you are given an average velocity (v ave ), it is the same thing as constant velocity: x = v ave t

Topic Overview Some objects have constant acceleration This means they are speeding up or slowing down The equations for constant acceleration: a = (v f -v i ) / t x = v i t + ½ at 2 v f 2 = v i 2 + 2ax

Topic Overview To solve problems with constant acceleration, make a table! ViVi Initial velocity VfVf Final velocity aAcceleration xDistance ttime Reminder: If an object is “at rest” Velocity = 0

Topic Overview Once you have made your table, choose the equation that does not have the “blocked off” variable. In this case, choose the equation that does not have t Reminder: If an object is “at rest” Velocity = 0 ViVi 0m/s VfVf 10m/s a9.8m/s 2 x? t? a = (v f -v i ) / t x = v i t + ½ at 2 v f 2 = v i 2 + 2ax

Sample Problem A 200kg car traveling at 10m/s hits the breaks and slows to rest at -5m/s 2. How far does the car travel while slowing down? Answer: 10m

Falling Objects

Topic Overview One example of a “constant acceleration problem” is a falling object (an object traveling through the air) All falling objects accelerate at 9.8m/s 2 due to gravity

Topic Overview Dropped objects start With zero initial velocity Objects thrown upward Have zero velocity at their Maximum height ViVi 0m/s VfVf a9.8m/s 2 x t ViVi VfVf 0m/s a9.8m/s 2 x t

Sample Problems A stone is dropped from a bridge approximately 45 meters above the surface of a river. Approximately how many seconds does the stone take to reach the water's surface? Answer: 3.03 sec

Projectile Motion

Topic Overview Objects that travel through the air in both the horizontal and vertical direction are called “projectiles”. These problems involve cars rolling off cliffs, objects flying through the air, and other things like that.

Topic Overview ▫ An object traveling through the air will: ▫ ACCELERATE in the VERTICAL DIRECTION  Because it is pulled down by gravity ▫ Have CONSTANT VELOCITY in the HORIZONTAL  Because there is no gravity ▫ Because they are different, we do calculations in the horizontal (x) and vertical (y)_ SEPARATELY.

Acceleration Velocity Horizontal Velocity Vertical -9.8m/s 2 Constant Increasing Zero Launch Angle Projectile Motion The time for an object to fall is determined by drop height ONLY (horizontal velocity has no effect)

Projectile Motion Horizontal Constant Velocity  x = vt Vertical Accelerating a = (v f -v i ) / t  x = v i t + ½ at 2 v f 2 = v i 2 + 2a  x TIME=TIME The key to solving projectile motion problems is to solve the horizontal and vertical parts SEPARATELY. Time is the only thing that is the same!

Sample Problem A bullet is shot at 200m/s from a rifle that is 2.5m above the ground. How far downrange will the bullet reach before hitting the ground? Step 1: Find the time. In this case we have to use the vertical height to find the time. Step 2: Use the time to find out the distance in the other direction (in this case the horizontal direction) Answer: 150m

Component Vectors

Topic Overview A vector is something that has both a magnitude (number value) and a direction.’ Examples of vectors are: Velocity Force Acceleration Momentum

Topic Overview All vectors at an angle can be broken up into “Component Vectors” Angled Vector (given value) Horizontal = X Component Vertical = Y Component

Topic Overview R  Can be any vector (Force, Velocity….) X Component: R(cosθ) Y Component R(sinθ) R(sinθ) R(cosθ) R R

Sample Problem A clown is launched from a cannon with an initial velocity of 40m/s. If the clown is launched at an angle of 30° from the horizontal, what are the initial vertical and horizontal components of the velocity? Answer: Vertical: 20m/s Horizontal: 34.6 m/s