KINEMATICS Chapter 3 KINEMATICS Study of the motion

KINEMATICS Chapter 3

KINEMATICS • Study of the motion of an object without considering outside factors which causes their motion.

KINEMATICS • Motion – denotes a change in position of a body with respect to some fixed point or reference point. • Speed – distance which a body traverse per unit time (scalar) • Velocity – displacement of a body per unit time (vector)

KINEMATICS •

KINEMATICS • Speed is equal to velocity if the body moves along a straight line (rectilinear motion). • If a body moves with equal displacement in equal intervals of time then the body is said to be moving with uniform motion. (v = constant)

KINEMATICS •

KINEMATICS • If magnitude of velocity is increasing, acceleration is positive; if decreasing, acceleration is negative (deceleration).

UNIFORMLY ACCELERATED MOTION •

UNIFORMLY ACCELERATED MOTION • When a body starts from rest, v 0 is zero and acceleration is positive. • If the body decreases in velocity, acceleration is negative, velocity becomes smaller than v 0 and when the body stops v = 0.

EXAMPLE How far does an automobile move while its speed increases uniformly from 15 mi/hr to 45 mi/hr in 10 s?

FREELY FALLING BODIES • The most common example of uniformly accelerated translation is that of body falling under the action of its own weight. • In the absence of air resistance, it is found that all bodies regardless of their size or weight; fall with the same acceleration at the same point on the surface of the earth.

FREELY FALLING BODIES Actual acceleration of falling objects depends on: • Location on the earth • Size and shape of the object • Density • State of atmosphere • Rotation of the earth

FREELY FALLING BODIES • a = g • At or near the earth’s surface g = 32. 17 ft/s 2 = 9. 806 m/s 2 = 980. 6 cm/s 2 • On the surface of the moon g = 1. 67 m/s 2 = 5. 47 ft/s 2 • Near the surface of the sun g = 274 m/s 2

FREELY FALLING BODIES •

FREELY FALLING BODIES • Acceleration of gravity is positive for bodies that are falling and negative for bodies that are thrown upward.

EXAMPLE A one-euro coin is dropped from the Leaning Tower of Pisa. It starts from rest and falls freely. Compute its position and velocity after 1. 0 s, 2. 0 s, and 3. 0 s.

MOTION IN A PLANE • A body that moves through space usually has a curved path rather than a perfectly straight one. • Projectile – any body that is given an initial velocity and then allowed to move under the influence of gravity. • Trajectory – the path followed by a projectile.