Change in VelocityChange in Velocity

You are probably most You are probably most familiar with the familiar with the velocity changes of a velocity changes of a moving bus or car.moving bus or car.

The rate at which The rate at which velocity (speed or velocity (speed or direction) changes direction) changes occur is called occur is called acceleration.acceleration.

Acceleration= Acceleration= final velocity- starting final velocity- starting velocityvelocity

timetime

Change in velocity = final Change in velocity = final – – starting starting

velocity velocity velocity velocity

Acceleration= Acceleration= change in velocitychange in velocity

timetime

Problem time!Problem time!

A car travelling at 60 km/s to the east A car travelling at 60 km/s to the east accelerates to 90 km/s to the east in 3 s. accelerates to 90 km/s to the east in 3 s. What is the car’s acceleration?What is the car’s acceleration?

Step 1: What we know!Step 1: What we know! Starting velocity Vi: 60 km/s, eastStarting velocity Vi: 60 km/s, east Final velocity Vf: 90 km/s, eastFinal velocity Vf: 90 km/s, east Time t: 3 sTime t: 3 s

Step 2: What equation/what are we Step 2: What equation/what are we finding?finding? a = (Vf – Vi)/ta = (Vf – Vi)/t

Problem continued!Problem continued!

Step 3: Put data into equation:Step 3: Put data into equation: a = (9 km/s – 6 km/s)/3 sa = (9 km/s – 6 km/s)/3 s We have chosen east as positive!We have chosen east as positive!

Step 4: Do the math!Step 4: Do the math! a= (3 km/s)/3 sa= (3 km/s)/3 s a= 1 km/sa= 1 km/s22

Step 5: Check the units and Step 5: Check the units and direction!direction!

PositivePositive acceleration acceleration

Negative Negative accelerationacceleration

Another Problem!Another Problem!

A car travelling at 60 km/s north A car travelling at 60 km/s north slams on the brakes to avoid hitting slams on the brakes to avoid hitting a deer. The car comes to a safe stop a deer. The car comes to a safe stop 6 s later. What is the car’s 6 s later. What is the car’s acceleration?acceleration?

Step 1: What we know:Step 1: What we know: Vi: 60 km/s northVi: 60 km/s north Vf:Vf: t: 6 st: 6 s

Problem 2 Continued!Problem 2 Continued!

Step 2: What equation/what are we trying to Step 2: What equation/what are we trying to find?find? a = (Vf – Vi)/ta = (Vf – Vi)/t

Step 3: Substitute the numbers in the Step 3: Substitute the numbers in the equation:equation: a = (0 km/s – 60 km/s)/6 sa = (0 km/s – 60 km/s)/6 s

Step 4: Do the math!Step 4: Do the math! a = (- 60 km/s)/6 sa = (- 60 km/s)/6 s a = - 1 km/sa = - 1 km/s22

What does the negative mean?What does the negative mean? Step 5: Check the units and direction.Step 5: Check the units and direction.

Constant Constant acceleration acceleration produces a produces a straight line when straight line when velocity and time velocity and time are graphedare graphed

The slope of the The slope of the line tells us the line tells us the accelerationacceleration

What if we need to know What if we need to know something else?something else?

A car experiences an acceleration of -3 A car experiences an acceleration of -3 km/s for 6 s. The car’s initial velocity was km/s for 6 s. The car’s initial velocity was 60 km/s to the south. What is its final 60 km/s to the south. What is its final velocity?velocity?

What can we do?What can we do? Step 1: What do we know?Step 1: What do we know?

Vi = 60 km/sVi = 60 km/s Vf = ?Vf = ? a = - 3 km/s a = - 3 km/s t = 6 st = 6 s

Step 2: What equation/what are we Step 2: What equation/what are we trying to find?trying to find? Start with what we know:Start with what we know:

a = (Vf – Vi)/ta = (Vf – Vi)/t Rearrange:Rearrange:

at = (Vf – Vi)at = (Vf – Vi) So at + Vi = VfSo at + Vi = Vf

Check to make sure the equation makes Check to make sure the equation makes sense!sense!

Vf = Vi + atVf = Vi + at

Step 3: Put the data in!Step 3: Put the data in! Vf = 60 km/s + (-3 km/sVf = 60 km/s + (-3 km/s22)(6 s))(6 s)

Step 4: Do the math.Step 4: Do the math. Vf = 60 km/s + (-18 km/s)Vf = 60 km/s + (-18 km/s) Vf = 42 km/s, southVf = 42 km/s, south

Step 5: Check the units (and Step 5: Check the units (and direction).direction).

Acceleration is fun!Acceleration is fun!

Gallardo LP560