Avergae speed = distance / time
Distance - time graphs
- The gradient shows the speed of the object - steeper gradient, higher speed
- Straight line - constant speed
- Curved line - changing speed
( u + v ) t
Acceleration = change in speed (or velocity) / time taken
The acceleration can be seen on a speed time graph - if the speed is increasing the object is accelerating and if the speed is decreasing the object is deccelerating
The area under the speed-time graph is equal to the distance travelled.
Velocity has a size (speed) and a direction therefore it is a vector
If two cars move past each other in opposite directions, their relative velocity is the sum of their individual velocities
If two cars move past each other in the same direction, their relative velocity is the difference of their individual velocities.
A vehicle needs to accelerate when going around a roundabout even though it's speed with stay the same, because the driver needs to apply a force towards the center of the roundabout.
Forces and motion
Force = mass x acceleration
- Reaction time increase by alcohol, distractions, travellign faster or being tired
- Breaking distance increased by road conditions, speed increase or poorly maintained car
- Safety when driving requires the driver to be the right distance away from the car infront and different speed limits used in different areas
Work and power
Work is done when a force moves an object in a certain direction.
Work done = force x distance moved
Weight is a measurement of the gravitational attraction on a body acting towards the centre of the Earth
Weight = mass x gravitational field strength
Power is the rate at which work is done
Power = work done / time taken
Cars with a more powerful engine have a higher fuel consumption and travel faster over the same distance. Therefore more fuel is required. Fuel pollutes the enviroment from the car exhaust (especially carbon dioxide). Power is also related to the force multiplied by the speed.
Energy on the move
Braking distance increases with speed (not proportioanally). When a car stops, the kinetic energy changes into heat in the brakes and tyres and road:
Work done by brakes = loss in kinetic energy
Braking force x braking distance = loss in kinetic energy
When the speed of the car doubles, the braking distance and kinetic energy quadruple; hence speed limits are enforced to reduce the risk of accidents.
Factors affecting fuel consumption: energy needed to increase kinetic energy, energy needed to work against friction, speed, how it is driven, road conditions.
Electrically powered cars use batteries and have a limited range, expensive to buy but recharging is cheap, solar-powered cars have a back-up battery. Battery powered cars don't give out harmful gases but the electricity needed for charging is made by burning fossil fuels. So are electrically powered cars any better for the enviromant?
Biofuels may reduce greenhouse gas emission but they cause deforestation - increased CO2.
Momentum (kgm/s) = mass (kg) x velocity (m/s)
To reduce injury the force on the person in the car should be as little as possible - momentum needs to be spread and time to come to a complete stop needs to increase.
Crumple zones, brakes, seat belts and air bags absorb some of the energy when the vehicle stops, change shape,reduce injury and reduce momentum therefore force.
The crumple zone is at the front and back of the car and it crumples on impact to absorb some of the energy. Seat belts stretch slightly so kinetic energy is converted to elastic energy. Air bags absorb some kinetic energy by squashing around them.
ABS brakes are a primary safety feature and send information from the wheels to a computer about the wheel spins so the pressure in the wheels can increase or decrease to stop the wheels skidding on the road by preventing them locking.
Cruise control and electric windows are also primary safety features.
When objects start to fall they accelerate because air resistance is small but weight is large. As they fall their speed increases, increasing the air resistance. When air resistance is balanced with weight terminal velocity/speed is reached and the object is travelling at a constant speed.
If the cross-sectional area of an object increases, the air resistance increases and therefore acceleration will decrease e.g. parachute jumping.
Drag racers and space shuttles use parachutes to slow them downn rapidly.
Gravitational field strength
The force of each kilogram on earth due to gravity is around 10N/kg.
The gravitational field strength: is unaffected by atomospheric conditions, is different in different positions on Earth e.g. higher near poles, and varies with the height above/below Earths surface.
The energy of games and theme rides
Any object held above the ground has gravitational potential energy GPE (J) = mgh
When a ball bounces GPE is converted to kinetic energy which is then converted to elastic potential energy. The ball will not return to the original height because energy has been transferred.
When terminal speed is reached, the kinetic energy has a maximum value and remains constant but gravitational potential energy is lost as they fall closer to the ground and work is done against friction.
A roller coaster at the top has a lot of GPE and when it is released, it is turned to kinetic energy. Each peak on a roller coaster is smaller than the last one because energy has been transferred to heat and sound due to friction and air resistance.
If speed doubles, KE quadruples.
If mass doubles, KE doubles.