Chapter 3 - motion

average speed

total distance/ total time

distance - time graphs

• time - x-axis

• distance - y-axis

• gradient = speed

• straight horizontal line - stationary

• straight sloping line - constant speed

instantaneous speed

• speed at a very short interval of time

• uses a tangent on a point from distance-time graph

• can also use a tangent for acceleration from velocity- time graph

displacement vs distance

• displacement - straight line path from beginning to end(0m if a circle) with direction

• distance - total distance travelled

average velocity

• change in displacement/ time taken

• vector quantity as displacement is a vector

acceleration

• rate of change of velocity

• change in velocity/ time

• ms-²

• vector - negative acceleration(deceleration) but magnitude may still be the same as acceleration

velocity time graphs

• velocity y-axis

• time x-axis

correlation between graphs of motion

• Velocity + acceleration in the same direction - speeding up

• Velocity + acceleration in different direction - slowing down

• Look at gradients to find significant points

• assume acceleration is uniformed acclerated motion(constant)

worked through example of correlation between graphs of motion

Graph of ball being thrown in the air and falling back down

• s-t graph — +ve gradient so +ve V, (0 gradient) approaches 0V, -ve gradient so -ve V

• ∴ v-t graph — +ve → 0 → -ve

• ∴ a-t graph — constant negative gradient so constant -ve acceleration

first half - +ve v, -ve a ∴ different direction so slowing down

second half - -ve v, -ve a ∴same direction so speeding up

equations of motion

• for motion in a straight line - uniformly accelerated motion

• “suvat” equations - symbols used

• (fromula booklet)

• a positive value of g used if the object is moving in the same direction as gravitational acceleration

kinematics

kinematics - study of motion of objects and their spatial relationships without any references to their masses or forces that cause them to change speed

Stopping distances

• thinking distance(distance travelled from when you first see a reason to stop to the moment when you use the brake)

• braking distance(distance travelled from the time when the brakes are applied and the vehicle stops)

Thinking distance

• thinking distance = speed x reaction time( a greater reaction time will mean a greater thinking distance is covered for a constant speed vice versa)

• linear relationship between speed + thinking distance

braking distance

• speed & braking distance is non linear relationship - as speed increases braking distances increases exponentially

• see this with the energy transfer - when a car breaks the kinetic energy of the car is transferred to the thermal energy in the brakes, the work done by the direction force = transfer of energy

• ↑Ek = Wd = F x s(distance moved by the car)

• ½ mv² = Fs showing the braking distance is directly proportional to the square of the car’s initial speed

Free fall & g

• gravity is the interaction between 2 objects with mass

• free fall - when an object is accelerating due to gravity with no other force acting on it

• denoted with g - ms-²

methods to determine g

• electromagnet + trapdoor → em magnet holds a steel ball over a trap door, when current is switched off a a timer starts, magnet is demagnetises and the ball falls through the trap door, electrical contact breaks and timer stop - calculate g with height + time taken

• light gates.→ 2 light beams one above the other connected to a timer, when ball passes through the first light game interrupts light beam and timer starts and when falls through the second light beam timer stops and there is a know distance.

• taking pictures → a small ball is dropped from rest next to a metre rule and the fall is recorded with rapid fire repeating mode OR a stroboscope illuminates the scene with rapid flashing producing a photo with multiple images of the falling ball, the position of the ball at regular intervals is then determined by examining the recording.

Problems with investigating g

electromagnet

• current is too high there will be a delay in releasing the ball after the current is switched off and the clock is triggered - turn off between measurements, adjust current, slight delays in timing

• If distance is too large or ball is too small air resistance may have a noticeable effect on the speed

• measuring the distance can cause uncertainty so measure accurately from the bottom of the ball accurately when held on the electromagnet to the top of the trap door

light gate(dropping card vertically through light gates)

• assumes that the card’s velocity is constant as it passes through the light gate → minimised by measuring the height fallen by the card to a line drawn horizontally across the middle of the card, rather then the top other bottom of the card

factors that increase thinking and braking distance

thinking

• higher speed

• tiredness

• alcohol + drugs

• distractions

• age of the driver

braking

• higher speed

• poor road conditions(icy or wet)

• poor condition of brakes

• poor condition of tyres

• mass of car(more people/luggage)

Miles and kilometres conversions

• 1 mile =1609.3 metres

• 1 hour =60 minutes = 3600 seconds

1mph =1.609 km/h 1609.3/3600 = 0.447ms^-1