Graphical Look at Motion: displacement – time curve The slope of the curve is the velocity The curved line indicates the velocity is changing – Therefore, there is an acceleration

Graphical Look at Motion: velocity – time curve The slope gives the acceleration The straight line indicates a constant acceleration

Graphical Look at Motion: acceleration – time curve The zero slope indicates a constant acceleration

Graphical Motion with Constant Acceleration A change in the acceleration affects the velocity and position Note especially the graphs when a = 0

Test Graphical Interpretations Match a given velocity graph with the corresponding acceleration graph Match a given acceleration graph with the corresponding velocity graph(s)

Galileo Galilei 1564 – 1642 Italian physicist and astronomer Formulated laws of motion for objects in free fall Supported heliocentric universe

Galileo Galilei (15 February 1564[2] – 8 January 1642)[1][3] was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy,"[4] the "father of modern physics,"[5] the "father of science,"[5] and "the Father of Modern Science."[6] Stephen Hawking says, "Galileo, perhaps more than any other single person, was responsible for the birth of modern science."[7] The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honour, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design. Galileo's championing of Copernicanism was controversial within his lifetime, when a large majority of philosophers and astronomers still subscribed (at least outwardly) to the geocentric view that the Earth remains motionless at the centre of the universe. After 1610, when he began supporting heliocentrism publicly, he met with bitter opposition from some philosophers and clerics, and two of the latter eventually denounced him to the Roman Inquisition early in Although he was cleared of any offence at that time, the Catholic Church nevertheless condemned heliocentrism as "false and contrary to Scripture" in February 1616,[8] and Galileo was warned to abandon his support for it—which he promised to do. When he later defended his views in his most famous work, Dialogue Concerning the Two Chief World Systems, published in 1632, he was tried by the Inquisition, found "vehemently suspect of heresy," forced to recant, and spent the rest of his life under house arrest.

Freely Falling Objects A freely falling object is any object moving freely under the influence of gravity alone. It does not depend upon the initial motion of the object – Dropped – released from rest – Thrown downward – Thrown upward

Acceleration of Freely Falling Object The acceleration of an object in free fall is directed downward, regardless of the initial motion The magnitude of free fall acceleration is g = 9.80 m/s 2 – g decreases with increasing altitude – g varies with latitude – 9.80 m/s 2 is the average at the Earth’s surface – The italicised g will be used for the acceleration due to gravity Not to be confused with g for grams

Acceleration of Free Fall, cont. We will neglect air resistance Free fall motion is constantly accelerated motion in one dimension Let upward be positive Use the kinematic equations with a y = -g = m/s 2

Free Fall – an object dropped Initial velocity is zero Let up be positive Use the kinematic equations – Generally use y instead of x since vertical Acceleration is – a y = -g = m/s 2 v o = 0 a = -g

Free Fall – an object thrown downward a y = -g = m/s 2 Initial velocity  0 – With upward being positive, initial velocity will be negative v o ≠ 0 a = -g

Free Fall -- object thrown upward Initial velocity is upward, so positive The instantaneous velocity at the maximum height is zero a y = -g = m/s 2 everywhere in the motion v = 0 v o ≠ 0 a = -g

Thrown upward, cont. The motion may be symmetrical – Then t up = t down – Then v = -v o The motion may not be symmetrical – Break the motion into various parts Generally up and down

Free Fall Example Initial velocity at A is upward (+) and acceleration is -g (-9.8 m/s 2 ) At B, the velocity is 0 and the acceleration is - g (-9.8 m/s 2 ) At C, the velocity has the same magnitude as at A, but is in the opposite direction The displacement is –50.0 m (it ends up 50.0 m below its starting point)