Constant Acceleration

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Presentation transcript:

Constant Acceleration

Graphs to Functions A simple graph of constant velocity corresponds to a position graph that is a straight line. The functional form of the position is This is a straight line and only applies to straight lines. x t x0 v t v0

Constant Acceleration Constant velocity gives a straight line position graph. Constant acceleration gives a straight line velocity graph. The functional form of the velocity is v t v0 a t a0

Top Fuel A top fuel dragster can reach 150 m/s (330 mph) in 3.7 s. What is the acceleration? In the equation v0 = 0 The acceleration is v/t. a = 41. m/s2 Credit: Lt. Col. W. Thurmond, U.S. Army

Acceleration and Position For constant acceleration the average acceleration equals the instantaneous acceleration. Since the average of a line of constant slope is the midpoint: v t a0(½t) + v0 ½t v0

Acceleration Relationships Algebra can be used to eliminate time from the equation. This gives a relation between acceleration, velocity and position. For an initial or final velocity of zero. This becomes x = v2 / 2a v2 = 2 a x from

Drag Strip A top fuel dragster accelerates at 40. m/s2 for 3.7 s. How far does the car go on the track? Starts at rest and at 0. x = 270 m Credit: Lt. Col. W. Thurmond, U.S. Army

Accelerating a Mass A loaded 747 jet has a mass of 4.1 x 105 kg and four engines. It takes a 1700 m runway at constant thrust (force) to reach a takeoff speed of 81 m/s (290 km/h). What is the force per engine? The distance and final velocity are used to get the acceleration. The acceleration and mass give the force.