MOTION IN ONE DIMENSION Mechanics: The study of motion of objects and related concepts of force and energy Kinematics: the description of how objects move Dynamics: deals with force and how objects move.

We will start our investigations with translational motion in one dimension. The moving object will be considered as a point like particle (point particle) Coordinate axis Finding its position relative to some reference point Locating an object

Change in position: displacement

SI BASE QUANTITIES AND UNITS Length meter m Time second s Mass kilogram kg a graph x plotted as a function of time. A good way to describe motion: For the displacement delta x = x2 – x1 = 10.0 m – 30.0 m, the displacement vector points to the left.

Average Velocity and Average Speed Q: How fast the object moves? Several quantities are associated with how fast. One of them Average velocity

Average speed is another quantity that can describe haw fast on object moves

Instantaneous Velocity Q: How fast a object moves at an instant?

v is the rate at which a particle’s positron x is changing with time at a given instant. v at an instant is the slope of the particle’s position-time curve.

ACCELERATION Change in velocity acceleration Average acceleration Instantaneous acceleration

If we combine it with the definition of v.

CONSTANT ACCELERATION Constant Acceleration – a common case vo – velocity at t=0 v – velocity at t *

same way v vo t as ** * and ** are called basic equations

Which quantities are in these equations? x-xo, v, vo, a, t On the other side each basic equation contains four of these 5th quantity - either given or an unknown In a typical problem, three of these quantities are given and 4th is asked to find. Note which quantity is given and which quantity is asked Then, use basic equations to derive a new equation which contains these quantities Two basic equations can be combined to give three other equations Each involves a different missing quantity

Eliminating t Eliminating a Eliminating vo

Independent of the object’s mass FALLING OBJECTS Galileo postulated that all objects would fall with the same constant acceleration like Independent of the object’s mass

a=-g=-9.80 m/s2 g=9.80 m/s2 Same transformation for the other four equations

Exercise A pitcher tosses a baseball up along y-axis with an initial speed of 12 m/s (a) How long does the ball take to reach its maximum height? (b) What is ball’s maximum height above its release point