Equations to describe motion with constant acceleration Kinematics Equations Equations to describe motion with constant acceleration

Describe the Motion.

vf vi The First Kinematic Equation Accelerating at a Derive an equation for vf vi v0 t

Derive an equation for Δx (think trapezoids…) The Second Kinematic Equation vf Derive an equation for Δx (think trapezoids…) vf ½ (vi+vf)t v0 vi vi t t

Derive an equation for Δx (without using vf) The Third Kinematic Equation Accelerating at a Derive an equation for Δx (without using vf) at ½ at2 vi v0 t vit vi t

The Fourth Kinematic Equation Using Substitution and Removing the variable “Time”

Variable Missing From Equation Which equation to use? Kinematic Equations Variable Missing From Equation displacment (Δx) acceleration (a) final velocity (vf) time (t)

A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26 A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26.8 m/s) in just 2.6 seconds. What is the acceleration of the Model S? How far will it travel while it is accelerating?

A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26 A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26.8 m/s) in just 2.6 seconds! a) What is the acceleration of the Model S? t = 2.6 s vi = 0 m/s (started from rest) vf = 26.8 m/s a = ? a = 10.3 m/s2

A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26 A Tesla Model S in “Insane Mode” can go from 0-60 mi/hr (0-26.8 m/s) in just 2.6 seconds! b) How far will it travel while it is accelerating? t = 2.6 s vi = 0 m/s (started from rest) vf = 26.8 m/s a = 10.6 m/s2 Δx = ? Δx = 34.8 m

A car traveling 16 m/s crashes into a telephone pole A car traveling 16 m/s crashes into a telephone pole. As the car’s front end crumples, the car moves forward 30 cm. Calculate the acceleration of the car.

A car traveling 16 m/s crashes into a telephone pole A car traveling 16 m/s crashes into a telephone pole. As the car’s front end crumples, the car moves forward 30 cm. Calculate the acceleration of the car. Δx = 0.30 m vi = 16 m/s vf = 0 m/s (ends at rest) a = ? a=-427 m/s2 a Δx

An airplane starts from rest and accelerates for 30 seconds before leaving the ground at the end of the 1.08 km runway. How fast was the plane going when it left the ground?

An airplane starts from rest and accelerates for 30 seconds before leaving the ground at the end of the 1.08 km runway. How fast was the plane going when it left the ground? t = 30 s vi = 0 m/s (started from rest) vf = ? a = ? Δx = 1080 m Vf = 72 m/s

Proportional Reasoning Problems A cheetah speeds up from rest with a constant acceleration and travels a distance of 10 m. How far will the cheetah travel if she had 3x the acceleration? How far will the cheetah travel in 3x the time?

x3 x3 x9 (x3)2 If “a” triples: If “t” triples: A cheetah speeds up from rest with a constant acceleration and travels a distance of 10 m. If “a” triples: If “t” triples: x3 x3 x9 (x3)2 Cheetah moves three times farther Cheetah moves nine times farther means “is proportional to”