P3

AVERAGE SPEED = DISTANCE X TIME

• GREATER THE SPEED OF OBJECT, FURTHER THE DISTANCE IT CAN TRAVEL IN A CERTAIN TIME
• GREATER THE SPEED OF OBJECT, SHORTER TIME IT TAKES TO GO A CERTAIN DISTANCE

AVERAGE SPEED = (U +V) / 2

• U = SPEED AT START
• V = SPEED AT END

DISTANCE = AVERAGE SPEED X TIME = ((U+V) X T) / 2

• UNIT OF SPEED = M/S
• MAY NEED TO CHANGE UNITS E.G. IF TIME IS GIVEN IN HOURS OR IF DISTANCE IS GIVEN IN KM
• 1000 M PER KM
• 3600 SECONDS IN AN HOUR

DISTANCE-TIME GRAPHS 

• GRADIENT = SPEED - STEEPER THE GRADIENT, FASTER OBJECT'S GOING
• FLAT SECTIONS - WHERE IT'S STOPPED
• NEGATIVE GRADIENT SECTIONS (DOWNHILL) MEANS OBJECT HAS CHANGED DIRECTION AND IS COMING BACK
• CURVES REPRESENT ACCELERATION AND DECELERATION
• CURVE OF INCREASING GRADIENT (STEEPENING) - ACCELERATING
• CURVE OF DECREASING GRADIENT (LEVELING OFF) - DECCELERATING
• STAIGHT UPHILL/DOWNHILL LINES - OBJECT MOVING AT STEADY SPEED

CALCULATING SPEED FROM A DISTANCE-TIME GRAPH JUST MEANS WORKING OUT THE GRADIENT OF THE LINE

SPEED = GRADIENT = (VERTICAL / HORIZONTAL)

USE SCALES OF AXIS TO DETERMINE VERTICAL AND HORIZONTAL NUMBERS

ACCELERATION = CHANGE IN SPEED / TIME TAKEN

• ACCELERATION - HOW QUICKELY SPEED IS CHANGING
• UNITS OF ACCELERATION - M/S2

SPEED AND VELOCITY

• SPEED - HOW FAST OBJECT IS GOING E.G. 30 MPH
• VELOCITY - SPEED AND DIRECTION OF OBJECT E.G. 30 MPH DUE NORTH
• NEGATIVE VELOCITIES - E.G. IF A CAR TRAVELING AT 20MPH TURNS AROUND, IT'S SPEED IS STILL 20 MPH BUT IT'S VELOCITY IS -20 MPH
• RELATIVE VELOCITY - DIFFERENCE IN VELOCITIES OF TWO OBJECTS TRAVELLING IN PARALLEL TO EACHOTHER E.G. TWO CARS TRAVELING AT 30 MPH PARALLEL TO EACHOTHER IN OPPISITE DIRECTION - RELATIVE VELOCITY IS THE DIFFERENCE BETWEEN THE TWO VELOCITIES = 30 AND -30 = 60 MPH

SPEED-TIME GRAPHS

• GRADIENT = ACCELERATION - THE STEEPER THE GRADIENT, THE GREATER THE ACCELERATION
• FLAT SECTIONS - STEADY SPEED
• POSITIVE GRADIENTS (UPHILL SECTIONS) - ACCELERATION
• NEGATIVE GRADIENTS (DOWNHILL SECTIONS) - DECELERATION
• AREA UNDER ANY SECTION OF GRAPH - DISTANCE TRAVELLED IN THAT TIME INTERVAL
• CURVE - NON UNIFORM ACCELERATION 
• 
• ACCELERATION - WORK OUT GRADIENT OF LINE - (VERTICAL / HORIZONTAL)
• SPEED - READ VALUE OFF SPEED AXIS
• DISTANCE TRAVELLED - AREA UNDER ANY PART OF GRAPH

FORCE = MASS X ACCELERATION

BALANCED FORCES - OBJECT WILL KEEP MOVING AT THE SAME SPEED IN THE SAME DIRECTION - TO KEEP GOING AT A STEADY SPEED, THERE MUST BE ZERO RESULTANT FORCE (IF CAR STARTS OFF STILL, IT'LL STAY STILL)

UNBALANCED FORCE - OBJECT WILL ACCELERATE IN THE DIRECTION OF THE FORCE - NEWTONS 2ND LAW OF MOTION - THERE WOULD BE A RESULTANT FORCE IF FORCES ARE UNBALANCED

ACCELERATION/DECELERATION - 5 DIFFERENT FORMS: STOPPING, STARTING, SPEEDING UP, SLOWING DOWN, CHANGING DIRECTION - ALL HAPPEN WHEN ARROWS ON FORCE DIAGRAM UNEQUAL

ANY RESULTANT FORCE PRODUCES ACCELERATION - IN MOST REAL SITUATIONS THERE ARE AT LEAST TWO FORCES ACTING ON OBJECT

RESULTANT FORCE OF TWO OBJECTS MOVING PARALLEL TO EACHOTHER - ADD OR SUBTRACT TWO FORCES

STOPPING DISTANCE = THINKING DISTANCE + BREAKING DISTANCE

THINKING DISTANCE 

THE DISTANCE A CAR TAVELS IN THE TIME BETWEEN THE DRIVER NOTICING THE HAZARD AND APPLYING THE BREAKS

FACTORS WHICH EFFECT THINKING DISTANCE

• HOW FAST YOU'RE GOING - HIGHER YOUR SPEED, HIGHER THE DISTANCE TRAVELLED IN THE TIME IT TAKES TO APPLY BREAKS
• HOW DOPEY YOU ARE - AFFECTED BY TIREDNESS, DRUGS, ALCOHOL, DISTRACTIONS, LACK OF CONCERNTRATION, CARELESS ATTITUDE

BREAKING DISTANCE

DISTANCE TRAVELLED IN TIME IT TAKES TO STOP ONCE BREAKS HAVE BEEN APPLIES

FACTORS WHICH EFFECT BREAKING DISTANCE

• HOW FAST YOU'RE GOING - SPEED EFFECTS TIME IT TAKES TO STOP
• MASS OF VEHICLE - WITH SOME BREAKS, BREAKING DISTANCE IS LONGER WHEN VEHICLE HEAVILY LOADED
• HOW GOOD THE BREAKS ARE - HOW MUCH FORCE APPLIED TO BREAKS, WHETHER BREAKS ARE FAULTY - BREAKS NEED TO BE CHECKED REGULARLY
• HOW GOOD THE GRIP IS - DEPENDS ON THREE THINGS
• - ROAD SURFACE - LEAVES, DIESEL SPILLS AND MUD ON THE ROAD - INCREASE BREAKING DISTANCE
• - WEATHER - WET OR ICY ROADS ARE SLIPPERY - INCREASE BREAKING DISTANCE 
• - TYRES - TREAD DEPTH OF TYRES SHOULD BE 1.6 MM MINIMUM - ESSENTIAL FOR GETTING RID OF WATER IN     WET CONDITIONS - TYRE WITH NO TREAD WILL RIDE ON SURFACE OF WATER AND EASILY SKID -                          AQUAPLANING - DANGEROUS

THE HIGHWAY CODE

• TO AVOID ACCIDENT, DRIVERS NEED TO LEAVE ENOUGH SPACE BETWEEN THEM AND THE CAR IN FRONT, RELATIVE TO THE SPEED THEY'RE GOING AT
• SPEED LIMITS - IMPORTANT - STOPPING DISTANCE IS HEAVILY EFFECTED BY SPEED
• ROAD CONDITIONS, WEATHER CONDITIONS AND TYRES CAN ALSO AFFECT THE STOPPING DISTANCE
• POLICE CALL DRIVING WITHIN STOPPING DISTANCE OF ANOTHER CAR "TAIL GATING"

EFFECT OF SPEED ON STOPPING DISTANCE

• THINKING DISTANCE - LINEAR - THINKING RATE INCREASES AT THE SAME RATE AS SPEED INCREASES - THIS IS BECAUSE THINKING TIME OF THE DRIVER STAYS PRETTY CONSTANT BUT THE HIGHER THE SPEED, THE MORE DISTANCE YOU TRAVEL IN THIS TIME (STRAIGHT LINE ON GRAPH)
• BRAKING DISTANCE - SQUARED RELATIONSHIP - INCREASES FASTER THE MORE YOU SPEED UP - AS SPEED DOUBLES, BREAKING DISTANCE INCREASES FOUR FOLD, WHEN SPEED TRBLES, BREAKING DISTANCE INCREASES 9 FOLD (CURVED LINE ON GRAPH)

WORK DONE = FORCE X DISTANCE

WHEN A FORCE MAKES AN OBJECT MOVE, ENERGY IS TRANSFERED AND WORK IS DONE

• WHEN SOMETHING MOVES, IT NEEDS ENERGY SUPPLIED BY SOMETHING ELSE TO MOVE IT
• THE THING WHICH MOVES THE OBJECTS A SUPPLY OF ENERGY E.G. FUEL, FOOD, ELECTRICITY
• WHEN IT DOES WORK TO MOVE THE OBJECT, IT TRANSFERS THE ENERGY IT'S RECIEVED (AS FUEL) INTO OTHER FORMS
• WHETHER ENERGY IS TRANSFERED USEFULLY (E.G. LIFTING A LOAD) OR WASTED (E.G. BY HEAT FROM FRICTION), YOU CAN STILL SAY THAT WORK IS DONE
• EXAMPLES OF WHEN WORK IS DONE INCLUDE LIFTING WEIGHTS, CLIMBING STAIRS, PUSHING A SHOPPING TROLLEY, PULLING A SLEDGE
• MEASURED IN JOULES

POWER = WORK DONE / TIME TAKEN

• POWER - THE MEASURE OF HOW QUICKLY WORK IS BEING DONE
• A POWERFUL MACHINE IS ONE THAT TRANSFERS A LOT OF ENERGY IN A SHORT SPACE OF TIME
• MEASURED IN WATTS - 1 WATT IS ONE JOULE OF ENERGY TRANSFERRED PER SECOND - 1 W = 1 J/S

POWER = FORCE X SPEED

• WORK DONE IS FORCE X DISTANCE
• POWER = (FORCE X DISTANCE) / TIME
• DISTANCE / TIME IS ANOTHER WAY OF WRITING SPEED
• POWER = FORCE X SPEED

FUEL CONSUMPTION

• CAR WITH LOW FUEL CONSUMPTION - E.G. 1L PER 100 KM - DOESN'T NEED MUCH FUEL TO TRAVEL 100KM - GOOD FOR ENVIRONMENT (LESS CO2 EMISSIONS) AND CHEAPER TO RUN
• CAR WITH HIGH FUEL CONSUMPTION - E.G. 1 MILE PER GALLON - ONLY TRAVELS 1 MILE FOR A GALLON OF FUEL - BAD FOR ENVIRONMENT, MORE EXPENSIVE

KINETIC ENERGY = 1/2 X MASS X SQUARED SPEED

• KINETIC ENERGY - ENERGY IT HAS WHEN MOVING - DEPENDS ON MASS AND SPEED OF OBJECT
• THE GREATER IT'S MASS AND THE FASTER IT'S GOING, THE BIGGER THE KINETIC ENERGY WILL BE

KINETIC ENERGY AND STOPPING DISTANCES

• KINETIC ENERGY TRANSFERRED = WORK DONE BY BRAKES
• 1/2 X M X V SQUARED = MAXIMUM BREAKING FORCE X BREAKING DISTANCE
• BREAKING DISTANCE INCREASES AS SPEED SQUARED INCREASES - IT'S A SQUARED RELATIONSHIP
• BECAUSE THE MAXIMUM BREAKING FORCE IS THE MAXIMUM AND CAN'T BE INCREASED, BREAKING DISTANCE MUST INCREASE BY A FACTOR OF FOUR TO MAKE THE EQUASION BALANCE
• IF YOU GO TWICE AS FAST, THE BREAKING DISTANCE MUST INCREASE BY A FACTOR OF FOUR TO CONVERT THE EXTRA KINETIC ENERGY
• INCREASING SPEED BY A FACTOR OF 3 INCREASES KE BY FACTOR OF 9 - BRAKING DISTANCE BECOMES 9 TIMES AS LONG
• DOUBLING THE MASS OF AN OBJECT DOUBLES THE KE - DOUBLE THE BREAKING DISTANCE

FOSSIL FUELS 

• MOST CARS RUN ON FOSSIL FUELS - PETROL OR DIESEL MADE FROM OIL (A FOSSIL FUEL)
• EMMISSIONS RELEASED WHEN FUELS ARE BURNED CAUSE ENVIRONMENTAL PROBLEMS - E.G. RELEASE CO2 WHICH LEADS TO GLOBAL WARMING, RELEASE SULFUR DIOXIDE WHICH LEADS TO ACID RAIN
• NON-RENEWABLE - ONE DAY THEY'LL RUN OUT

BIOFUELS

• CARS RUN ON FUELS MADE FROM PLANTS AND ORGANIC WASTE
• SCIENTISTS WORKKING ON ALTERNATIVES TO FOSSIL FUELS 
• ADVANTAGES - RENEWABLE, CARBON NUETREL - RELEASE AS MUCH CARBON DIOXIDE AS PLANTS TAKE IN WHEN GROWING - OVERALL CO2 EMISSIONS WOULD BE REDUCED IF WE SWITCHED TO BIOFUELS
• DOESN'T PRODUCE MUCH OTHER POLLUTION BUT CARS THEMSELVES PRODUCE POLLUTION WHEN MADE

ELECTRIC CARS

• CARS THAT RUN ON LARGE BATTERIES THAT POWER ELECTRIC MOTORS
• DON'T RELEASE POLLUTION WHEN DRIVING BUT NEED TO BE CHARGED - CHARGED WITH ELECTRICITY GENERATED IN POWER STATIONS WHICH DO POLLUTE
• WAY ROUND THIS - SOLAR POWER - COULD REDUCE OVERALL CO2 EMMISSIONS - DISADVANTAGE - SOLAR PANELS EXPENSIVE TO MAKE AND BUY
• DISADVANTAGES OF ELECTRIC CARS - OVERALL PRODUCTION OF CARS STILL POLLUTE AND ELECTRIC CARS ARE CURRENTLY LIMITED IN PERFORMANCE COMPAIRED TO FOSSIL FUELED CARS
• THIS IS CHANGING, HOWEVER, WITH ADVANCES IN TECHNOLOGY AND NEW DESIGNS

FACTORS WHICH EFFECT FUEL CONSUMPTION

• MASS AND SPEED -TO MOVE A CAR, FUEL NEEDS TO BE CHANGED INTO KINETIC ENERGY - KINETIC ENERGY = MASS X SPEED SQUARED X 1/2 SO THE HIGHER THE SPEED AND HIGHER THE MASS, THE MORE KINETIC ENERGY IT WILL NEED AND THE MORE FUEL IT WILL NEED TO BE TURNED INTO K.E.
• CARS WORK MORE EFFICIENTLY AT CERTAIN SPEEDS - MOST EFFICIENT SPEED BETWEEN 40 AND 55 MPH
• DRIVING STYLE - ACCELERATION USES MORE K.E. SO MORE FUEL WILL NEED TO BE TURNED INTO K.E. - CONSTANT BRAKING AND ACCELERATING ALSO INCREASES K.E. NEEDED
• WEATHER CONDITIONS - DIFFERENT WEATHER AND ROAD CONDITIONS MAY REQUIRE MORE FREQUENT BRAKING AND ACCELERATION
• FRICTION - CAR USES K.E. FROM FUEL TO WORK AGAINST FRICTION BETWEEN TYRES AND ROAD AND BETWEEN THE CAR ITSELF AND THE AIR AROUND IT - OPENING WINDOWS, HAVING A ROOF BOX ETC. WILL HAVE AN EFFECT - INCREASES AIR RESISTANCE AND DRAG
• CARS DESIGNED TO BE MORE FUEL EFFICIENT - MORE EFFICIENT ENGINES, STREAMLINED
• HIGHER FUEL CONSUMPTION RELEASES MORE EMMISSIONS - WORSE FOR ENVIRONMENT - CAR MANUFACTURERS CHANGING CAR AND ENGINE DESIGNS TO REDUCE EMISSIONS

MOMENTUM (KGM/S) = MASS (KG) X VELOCITY (M/S)

• HIGHER THE SPEED AND LARGER THE MASS OF AN OBJECT, THE MORE MOMENTUM IT HAS

FORCE ACTING = CHANGE IN MOMENTUM (KGM/S) / TIME TAKEN FOR CHANGE TO HAPPEN (S)

• CAN BE EXPLAINED BY NEWTONS SECOND LAW OF MOTION (FORCE = MASS X ACCELERATION)
• ANY FORCE APPLIED TO OBJECT INCREASES IT'S ACCELERATION (F = MASS X A)
• ACCELERATION IS A CHANGE IN VELOCITY OVER TIME (A = CHANGE IN V / T)
• THEREFORE A FORCE APPLIED TO AN OBJECT CHANGES IT'S VELOCITY OVER TIME (F = CHANGE V X MASS / T)
• A CHANGE IN MOMENTUM CAN BE CAUSED BY A CHANGE IN VELOCITY (CHANGE IN M = MASS X CHANGE IN V) SO ANY FORCE APPLIED TO AN OBJECT OVER A CERTAIN TIME CAUSES A CHANGE IN MOMENTUM (F = CHANGE IN M / T)

EFFECT OF TIME TAKEN FOR CHANGE IN MOMENTUM ON FORCE

• IF MOMENTUM CHANGES VERY QUICKLY, FORCE APPLIED WILL BE VERY LARGE - DANGEROUS
• LONGER IT TAKES FOR CHANGE IN MOMENTUM, SMALLER THE FORCE

CAR SAFETY FEATURES

• COLLISION - FORCE ON OBJECT CAN BE LOWERED BY SLOWING OBJECT DOWN OVER LONGER TIME - LONGER IT TAKES FOR CHANGE IN MOMENTUM, SMALLER FORCE ACTING - SOME INJURIES CAUSED BY RAPID DECELLERATION OF PARTS OF BODY - INCREASING COLLISION TIME REDUCES DECELERATION
• SAFETY FEATURES INCREASE COLLISION TIME - REDUCE FORCES AND DECELLERATION - REDUCE INJURY - ALSO REDUCE INJURIES BY STOPPING PERSON HITTING HARD SURFACES INSIDE CAR - SOME FEATURES CHANGE SHAPE DURING CRASH - ABSORB KINETIC ENERGY
  • CRUMPLE ZONES - CRUMPLE AND CHANGE SHAPE ON IMPACT - INCREASE TIME TAKES CAR TO STOP
  • SEAT BELTS - STRETCH - INCREASE TIME TAKEN FOR WEARER TO STOP - REDUCES FORCE ACTING ON CHEST - NEED TO BE REPLACED AFTER CRASH
  • AIR BAGS - SLOW PERSON DOWN MORE GRADUALLY
• ROADS MADE SAFER - PLACING CRASH BARRIERS AND ESCAPE LANES IN DANGEROUS LOCATIONS - DESIGNED TO INCREASE TIME AND DISTANCE OF COLLISION - FORCE REDUCED

ABS BRAKES - ANTI-LOCK BRAKING SYSTEM BRAKES - KEEP CONTROL OF CARS STEERING WHEN BRAKES HARD

• DRIVER BRAKES HARD - ORDINARY BRAKES LOCK WHEELS - CAN'T TURN - CAN CAUSE SKID
• ABS PUMP ON, OFF - STOP WHEELS LOCKING - PREVENT SKIDDING - GIVE CAR SHORTER BREAKING DISTANCE

TESTING SAFETY FEATURES

• SAFETY FEATURES RIGOROUSLY TESTED - SEE HOW EFFECTIVELY THEY SAVE LIVES OR STOP INJURIES
• TEST INVOLVES CRASHING CARS CONTAINING CRASH TEST DUMMIES WITH AND WITHOUT SAFETY FEATURES - WATCHING SLOW MOTION FILM FOOTAGE TO SEE RESULTS - SEE HOW BAD INJURY WOULD BE
• REPEATED USING DIFFERENT CARS, SPEEDS, SIZED DUMMIES
• RESULTS COMPARED WITH REAL DATA FROM ACTUAL CAR ACCIDENTS - TAKEN INTO ACCOUNT WHEN DECIDING WHETHER TO FIT SAFETY FEATURE
• CRASH TESTS - SHOWM WEARING SEATBELTS REDUCES FATALITIES BY 50% - AIRBAGS REDUCE 30%
• DEPARTMENT FOR TRANSPORT PRODUCE REPORTS ON ROAD TRAFFIC ACCIDENTS IN UK EACH YEAR - SHOW SIGNIFICANT REDUCTION IN DEATHS AND INJURIES SINCE 1980S - DUE TO WIDE RANGE OF SAFETY FEATURES

FRICTION - FORCE WHICH ACTS AGAINST OBJECTS THAT ARE MOVING, SLOWING THEM DOWN

• FRICTIONAL FORCE - MATCH SIZE OF FORCE TRYING TO MOVE IT UP TO POINT - AFTER POINT FRICTION WILL BE LESS
• FRICTION ACTS TO MAKE OBJECT SLOW OR STOP - ALWAYS NEED DRIVING FORCE TO KEEP STEADY SPEED
• WAY IN WHICH FRICTION OCCURS:LARGER AREA OF OBJECT, GREATER DRAG - DRAG REDUCED BY BY STREAMLINING E.G. SPORTS CARS ARE WEDGE SHAPED - ROOF BOXES AND DRIVING WITH WINDOWS OPEN RUIN THIS - INCREASE DRAG
  • BETWEEN SOLID SURFACES WHICH ARE GRIPPING
  • BETWEEN SOLID SURFACES WHICH ARE GLIDING PAST EACHOTHER
  • RESISTANCE OR DRAG FROM FLUIDS
• SOMETHING DESIGNED TO REDUCE SPEED E.G. PARACHUTE - LARGE SURFACE AREA - MORE AIR RESISTANCE
• IN A FLUID, FRICTION ALWAYS INCREASES AS SPEED INCREASES

TERMINAL SPEED - MAXIMUM SPEED REACHED BY FALLING OBJECTS WHERE THEY NO LONGER ACCELERATE

• OBJECT FIRST SETS OFF - MORE FORCE ACCELERATING OBJECT THAN INCREASING SPEED 
• AS SPEED INCREASES, AIR RESISTANCE INCREASES - GRADUALLY REDUCES ACCELERATION UNTIL RESISTING FORCE EQUAL TO ACCELERATING FORCE - FORCES BALANCED - NO FURTHER ACCELERATION

TERMINAL SPEED IN RELATION TO DRAG

• TERMINAL SPEED OF ANY MOVING OBJECT DEPENDS ON DRAG COMPARED TO DRIVING FORCE
• GREATER DRAG (DEPENDS ON SHAPE AND AREA OF OBJECT) - LOWER TERMINAL SPEED
• SKYDIVERS HAVE PARACHUTES - INCREASE AIR RESISTANCE DUE TO LARGE SURFACE AREA BUT SAME AMOUNT OF DRIVING FORCE - EQUAL OUT QUICKER - DECREASE TERMINAL SPEED - MAKE LANDING SAFE

FORCES AND SPEED

• STEADY HORIZONTAL SPEED - REACTION, WEIGHT, THRUST, WEIGHT BALANCED
• STEADY VERTICAL SPEED - WEIGHT AND DRAG BALANCED
• HORIZONTAL ACCELERATION - UNBALANCED FORCES - THRUST BIGGER THAN DRAG
• VERTICAL ACCELERATION - FORCES UNBALANCED - WEIGHT BIGGER THAN DRAG

GRAVITATIONAL POTENTIAL ENERGY = MASS X G X HEIGHT

• GPE - ENERGY THAT SOMETHING HAS BECAUSE OF IT'S HEIGHT ABOVE THE GROUND - ENERGY USED TO RAISE IT STORED AND CONVERTED TO KINETIC ENERGY AS IT FALLS
• G = GRAVITATIONAL FEILD STRENGTH - ON EARTH IT'S ABOUT 10

K.E GAINED = G.P.E LOST - mgh = ¹/₂ mv²

• WHEN FALLING OBJECT REACHES TERMINAL SPEED, G.P.E CAN'T BE CONVERTED TO K.E TO MAKE IT ACCELERATE ANYMORE - CONVERTED TO INTERNAL ENERGY OF OBJECT OR USED TO HEAT UP AIR PARTICLES SURROUNDING IT THROUGH FRICTION
• EQUASION CAN BE REARRANGED TO H = V SQUARED / 2G (AS LONG AS MASS DOESN'T CHANGE WHEN FALLING)
• CAN BE USED TO FIND HEIGHT SOMETHING IS DROPPED FROM TO REACH CERTAIN SPEED E.G. WHEN DESIGNING ROLLAR COASTER

ROLLAR COASTERS

• AT TOP OF ROLLARCOASTER - CARRIAGE HAS LOTS OF GPE
• CARRIAGE DESCENDS - GPE CONVERTED TO KE - CARRIAGE SPEEDS UP
• IGNORING AIR RESISTANCE AND FRICTION BETWEEN TRACK AND CART, MINIMUM GPE AND MAXIMUM KE AT LOWEST POINT OF ROLLARCOASTER
• REAL ROLLAR COASTER - DOES HAVE FRICTION - CARRIAGE HAS TO HAVE ENOUGH KE TO GET UP HILL AGAIN