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Uniformly Accelerated Motion Galileo Galilei (15641642) Hypothesis: At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration. •Free Fall—the motion of a body when only the force due to gravity is acting on the body. •The force due to gravity is constant. •Because the force of gravity is constant, the acceleration due to gravity is also constant. •Acceleration due to gravity on Earth is denoted with the symbol g and has a magnitude of 9.80 m/s2. •In British units, g = 32 ft/s2. •Air resistance is often considered negligible when we are analyzing freelyfalling bodies. •However, if the velocity becomes very large, air resistance can also become large. •A constant maximum velocity can be reached when an object is falling in air called terminal velocity. •This occurs as the air resistance increases enough to equal the force to gravity. •Remember: the acceleration due to gravity is a vector quantity. Therefore, it has magnitude and direction. •Its magnitude is 9.80 m/s2 with a direction downward toward the center of Earth. •It is extremely important to pay attention to your frame of reference (what direction motion is), here. Assign +/- to your acceleration! •Most of the time, g will be negative because it is a downward acceleration. •Since g is a constant acceleration, we can use our kinematic equations to solve for a missing quantity… •Substitute g for a •For vertical motion, use y in place of x. 1 D Kinematics Alphabet Soup...what do these letters mean! a = acceleration d = distance or displacement g = acceleration due to gravity s = speed t = time v = velocity xi = initial position xf = final position Basic Kinematic Equations Kinematic equations with muscle! d = x f - xi s = d/t vf = vi + at v = d/t xf = xi + vit + ½ at2 a = (vf - vi)/t vf2 = vi2 + 2a(xf – xi) vavg = 1/2 (vf + vi) •It is arbitrary whether we choose y to be positive in the upward direction or in the downward direction; but we must be consistent about it throughout a problem’s solution. •Practice, Practice, Practice!!! One of the fastest airplanes is the Lockheed SR-71. If an SR-71 flies 15.0 km west in 15.3 s, what is its average velocity in km per hour? Where do we start??? 1. Write the given information. 2. Decide what to solve for. 3. Check units for any conversions. 4. Substitute values and do the math. 5. Check work and units. A walrus accelerates from 7.0 km/h to 34.5 km/h over a distance of 95 m. What is the magnitude of the walrus’s acceleration? A bicyclist accelerates--0.870 m/s2 during a 3.80 s interval. What is the change in velocity of the bicyclist and bicycle?