3.1: Motion

Speed

Speed

A scalar quantity
Total ground covered

Displacement

Vector quantity

Measures distance travelled in a particular direction

Speed equation

Distance travelled/time

Displacement equation

Total displacement/time

Distance (compare and contrast)

How much ground is covered in total

Displacement (compare and contrast)

The shortest possible distance between two points

Point of instantaneous velocity

To overcome the fact that average speed doesn’t tell you whether speed changes over the total time period

Instantaneous Velocity/Speed

Velocity/Speed of an object measured over a very short period of time

How instantaneous velocity works

V=Δs/Δt

If it keeps getting smaller you get speed at an instant

How to find instantaneous velocity

Use a tangent to find the gradient of a graph at a point

Acceleration Definition

The rate of change of velocity

What type of quantity is acceleration

Acceleration is a vector quantity

Units of acceleration

ms^-2

Equation for acceleration

(final velocity - initial velocity) / time

Δv / Δt

Objects with high acceleration

• Rockets

• F1 cars

  • Falling objects

Distance-time graph

• Distance on y-axis

• Time on x-axis

• Gradient is speed

• Stationary objects represented with horizontal line

  • Objects moving with a constant speed are represented with a straight line with a constant gradient

Displacement-time graph

• Displacement on y axis

• Time on x-axis

• Gradient is velocity

• Stationary objects represented by a horizontal line

• Moving objects represented by a sloping line

Velocity-time graph

• Time on x-axis

• Velocity on y-axis

• Gradient is acceleration

• Area under graph is displacement

S.U.V.A.T equation without displacement

v=u+at

S.U.V.A.T equation without final velocity

s=ut + 1 / 2at²

S.U.V.A.T equation without acceleration

s=1 / 2(u+v)t

S.U.V.A.T equation without time

v²=u²+2as

When do we use S.U.V.A.T equations?

When objects are moving at a constant acceleration with a changing velocity

When is an object in free fall?

When an object is accelerating under gravity with no other forces acting on it

What is the acceleration of free fall?

9.81ms^-2

What is an electromagnet

• Electromagnet holds a small steel ball above a trap door

• When current is switched off, timer is triggered and electromagnet demagnetises causing the ball to drop

• When the ball hits the trap door, electrical contact is broken and timer stops

Method for determining the acceleration of free fall (electromagnet)

1. Measure height of fall with a ruler

2. Record time of fall using timer

3. Use s=ut+1 / 2at² where s=h, v=0ms^-1 and a=g to calculate acceleration of free fall

What is a light gate?

Two light beams one above another, with detectors connected to a timer. When ball falls through the first beam, it interrupts the signal and the timer starts. When the ball falls through the second beam, a known distance below, the timer stops

Method for determining the acceleration of free fall (light gates)

1. Measure the height of fall with a ruler

2. Record the time of fall using the stop clock

3. Use s=ut+1 / 2at² where s=h, u=0ms^-1 and a=g to calculate acceleration of free fall

Picture method for determining the acceleration of free fall

• Drop a small metal ball from rest next to a metre ruler

• Its fall is recorded on video with a camera in rapid fire, repeating mode

• Camera shutter is held open, which produces a photograph with multiple images of the falling ball

• The position of the ball at regular intervals is then determined by examining the recording

Graphical method for determining the acceleration of free fall

1. Measure the height of fall with a ruler

2. Record the time of fall with a stop clock

3. Plot a graph with height on y-axis and t² on x-axis

4. Use y=mx+c analysis to find g

Thinking Distance

• Distance vehicle travels in the time that it takes for a driver to react to a situation

• Thinking distance=speed x reaction time

Factors affecting thinking distance

Condition of the driver (which affect reaction time like alcohol levels):

• Alcohol

• Tiredness

• Drugs

• Distractions

Braking distance

• The distance a vehicle travels whilst the brakes are applied and the vehicle is decelerating to a stop

• Braking distance= (speed)^-2/-2 x deceleration

Factors affecting braking distance

Condition of vehicle and road:

• Road surface conditions

• Worn tyres

• Brakes conditions

• Larger mass vehicles

Stopping distance

The sum of the thinking and braking distances

Horizontal and vertical forces in projectile motion

The vertical and horizontal components are independent of each other

Projectile motion, assuming no air resistance

• Vertical velocity changes due to the acceleration of freefall

• Vertical displacement and time of flight can be calculated with SUVAT equations

• Horizontal velocity remains constant

Key points on projectiles fired at an angle to the vertical

• Only V_y is affected by acceleration of freefall so this continually changes

• V_v= maximum at take off and just before it lands= -maximum

• V_v= 0 at maximum height

• The time taken to reach max height is half the total time of flight

V_y and V_x components of velocity (projectiles fired at an angle to the vertical)

• Vertical component= V_y = Vsinθ

• Horizontal component= V_x = Vcosθ

Steps to solve distance travelled (projectiles fired at angle to the vertical)

1. Draw vector triangle, find v_x and v_y components

2. Calculate time for max height

3. Multiply by 2 to get total time

4. Use s=d/t to find distance travelled