By Wesley C Becker
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5 ONE-DIMENSIONAL MOTION WITH CONSTANT ACCELERATION a Many applications of mechanics involve objects moving with constant acceleration. This type of motion is important because it applies to numerous objects in nature, such as an object in free fall near Earth’s surface (assuming that air resistance can be neglected). 15a. When an object moves with constant acceleration, the instantaneous acceleration at any point in a time interval is equal to the value of the average acceleration over the entire time interval.
0 m, the rocket’s engines start and provide constant upward acceleration until the rocket lands. What acceleration is required if the speed on touchdown is to be zero? com and clicking on the Pre-Test link for this chapter. 1] where xi is the initial position of the object and xf is its final position. A vector quantity is characterized by both a magnitude and a direction. A scalar quantity has a magnitude only. 5 One-Dimensional Motion with Constant Acceleration The average speed of an object is given by Average speed ϵ The most useful equations that describe the motion of an object moving with constant acceleration along the x axis are as follows: total distance total time The average velocity v during a time interval ⌬t is the displacement ⌬x divided by ⌬t.
4 m/s2, and we can use the kinematic equations with constant acceleration a to find the height and velocity of the rocket at the end of phase 1, when the fuel is burned up. 80 m/s2, with initial velocity and position given by the results of phase 1. Apply the kinematic equations for free fall. 10) Two linked phases of motion for a rocket that is launched, uses up its fuel, and crashes. 00 s. 00 s into Equations (3) and (4) to find the rocket’s velocity v and position y at the time of burnout. These will be called vb and yb , respectively.