One-Dimensional Motion

ACCELERATION AND UNIFORMLY ACCELERATED MOTION

One-Dimensional Motion

One-Dimensional MotionACCELERATION

Objectives

• Define acceleration• Solve acceleration problems• Draw and interpret velocity versus time and acceleration versus time

graphs

Acceleration

• The speeding up or slowing down of an object• The rate that velocity changes, so the change in velocity over the change in time• a= Δv/Δt = V f – V i / t f – t I

• Units- m/s2

• Vector or scalar?

Instantaneous Versus Average

• Average acceleration-change in velocity over an interval of time• Instantaneous Acceleration-change in velocity at an instant of time

Example

• A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?

Example

• I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds. What is the acceleration?

Example

• A runner starts at a velocity of 1.2 m/s and speeds up constantly during a workout at a rate of 0.2m/s2. After 25 minutes what is the speed of the runner?

Velocity Versus Time Graph

• Velocity

• Time• Slope=rise over run• What does slope indicate here?

Example

• Velocity

• Time• What does this tell us about the acceleration?

Example Continued

• Accel

• time

Acceleration is __________ and is below the time axis because _________________

Example Continued

• What does the distance versus time graph look like?

Example

• Velocity

• Time• Draw the acceleration vs time graph and the position vs time

Example Continued A-T graph

Example Continued- D-T graph

• Position Versus Time graph• Slope=velocity• +slope=movement to the right/up• -slope=movement to the left/down• Linear=constant velocity, no acceleration

Review

• Velocity Versus Time Graph• Slope=acceleration• +slope=speeding up• -slope=slowing down• Slope DOES NOT indicate direction here• Slope of 0=no acceleration• If the line is above the time axis the object is moving to the right• If the line is below the time axis the object is moving to the left• Straight line=constant accleration

Review

• Acceleration Versus Time Graph• Straight horizontal line=constant acceleration• Below the X axis=slowing down• Above the X axis=speeding up

Review

One-Dimensional Motion UNIFORMLY ACCELERATED MOTION

Objectives

• Solve problems using uniform acceleration equations

Uniformly Accelerated Motion

• Acceleration is constant• What would a velocity versus time graph look like with constant

acceleration? Without constant? • Equations• V f = V i + at• Δx = V i Δt + ½ (a t2)• Vf

2 = Vi2 + 2 a Δx

• Δx = ½ (Vf + Vi) Δt • What variables do we have?

Example

• How long must a runway be for a plane to reach a takeoff velocity of 75 m/s if it accelerates at 20 m/s2?

Example

• My tea tumbler falls off my car and slides along 95 South for 75 m. Friction slows my tumbler at 6 m/s2.• A)How fast was the car moving when the tumbler fell?• B)How long did it take the tumbler to stop?

• A police car chases after a robber who is moving at 50 m/s East. If the police car starts out going 5 m/s east, and accelerates at 8 m/s2 east for 6 seconds. What will be the velocity of the police car after 3 seconds?• How far will the police car travel?• How far will the robber travel in the same time if he

does not accelerate?

Example

One-Dimensional MotionFREEFALL

Objectives

• Define freefall• Solve freefall problems

Freefall

• If the only force acting upon an object is gravity the object is said to be in freefall• No _________________• Considered to be uniform accelerated motion• g is the acceleration due to gravity= 9.8 m/s2

• When an object is in freefall we will use -9/8 m/s2

• Does mass matter?• What would a distance versus time graph look like for a ball being

thrown in the air?

Example

• A ball is dropped from a height of 2.0 m. What is the velocity before it strikes the ground? How long did it take to hit the ground?

Example Cont

• Draw the position, velocity, and acceleration graphs

Example continued

• How long would it take for the same ball to be thrown up 2m and then fall to the ground?

Example

• A ball is thrown straight down with a speed of 0.50 m/s from a height of 4.0 m. What is the speed of the ball 0.70 seconds after the ball is released?

Example

• A 0.25 kg baseball is thrown upward w/ a speed of 30 m/s. Neglect friction. What is the maximum height that the baseball reaches?