SPEED AND ACCELERATION MOTION SPEED Average speed Calculates

SPEED AND ACCELERATION MOTION

SPEED Average speed- Calculates the average speed of a total distance • s= ∆d/∆t • ∆d/∆t= (df-di)/(tf-ti)

COMPONENTS • Let's examine this: • ∆d/∆t= (df-di)/(tf-ti) • Whenever you have a change in something, you can break that thing down into its components, final and initial.

VELOCITY VS SPEED • Speed is a SCALAR. Speed is a measurement independent of the coordinate system. • Velocity is a VECTOR. Velocity is a measurement of speed that depends on the coordinate system. This means that velocities include a DIRECTION and MAGNITUDE.

VELOCITY AND ACCELERATION Since we now know about Scalars and Vectors, let's change up the Speed Equation to deal with Velocity. • v= ∆d/∆t • ∆d/∆t= (df-di)/(tf-ti) Therefore: • Acceleration- change in speed or direction • a= ∆v/t • a=(vf-vi)/t

GRAVITY AND FREE FALL • Gravity is an acceleration. • When an object is falling, it falls at an acceleration of 9. 8 m/s 2, no matter the mass or density. • When no other factors are affecting an object as it falls, it said to be in a “free fall. ” • To calculate height when dealing with an object in free fall, use this equation: • d = (vi * t) + (1/2 * a* t^2)

DECELERATING UP. . . ACCELERATING DOWN • When an object is thrown upward, it starts with an initial velocity (vi) of whatever it is tossed at. Due to gravity, it decelerates on the way up, until it reaches its max height. • At max height, the object has 0 velocity (this is sometimes used as the object's vf or final velocity). • A moment after reaching its max height, again, due to gravity, the object will begin to fall. This is an acceleration as well. • The object's final velocity (vf) when it reaches the ground will be equal to its initial velocity.

TIME INDEPENDENT ACCELERATION • Sometimes you'll need to handle velocity and acceleration without using time. To do so, we use this equation: • vf^2 =vi^2 + 2 ad • d stands for distance and will sometimes be represented by x or y, depending on which direction it's going. • d = (df – di)

ALL OUR EQUATIONS! • Velocity: • v= ∆d/∆t • ∆d/∆t= (df-di)/(tf-ti) • vf^2 =vi^2 + 2 ad • Distance: • d = d f – di • Height: • d = (vi * t) + (1/2 * a * t^2) • Acceleration: • a= ∆v/t • a=(vf-vi)/t

EXAMPLES • Isaac decides to show off his car. He jumps in his car and hits the gas! The car accelerates from 0 m/s to 32 m/s in 7 seconds. What is its acceleration?

EXAMPLES • Jason thinks he’s got a faster care than Isaac. To prove it, he hops in his car and starts to drive. He accelerates at a rate of 2. 5 m/s 2 from 27 m/s to 36 m/s. How long does this take? Is Jason faster? Who’s acceleration is better?

EXAMPLES • Dahira goes to Six Flags and decides to ride their new roller coaster, El Diablo. As it loops, it takes 6 seconds for the roller coaster to go from 0 m/s to 40 m/s. What is its acceleration?

EXAMPLES • Gabby kicks a soccer ball vertically upward from the ground at 5 m/s. How high above the ground does the soccer ball reach? How much time does it take to go from the ground to its highest point?

EXAMPLES • Keshawn is practicing for the NFL combine. He decides to work on his vertical. Keshawn can jump straight up a height of 0. 940 m. What is his initial velocity as he leaves the ground, and how much time was he in the air?