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Extra resources for Dynamics: SI Version: Engineering Mechanics
5) as dv = aCt) dt and integrate in terms of definite integrals: r Jro dv = [' a(t)cli lto The lower limit Vo is the velocity at time to, and the upper limit v is the velocity at an arbitrary time t. O L where the lower limit is the position at time to and the upper limit s is the position at an arbitrmiY time t. 10). 4). 7(a)). 7(b)). :eleration and velocity of P and changes in its velocity and position, You can often use these relationships to obtain a qualitative understanding of an object's motion, and]lin some cases you can even use them to determine its motIOn.
38, what distance does the boat move in the 2 s following the shutdown of its cngine? 40 A ~leel ball is released from rest in a container of oil. 9g - Ct), where g is the acceleration due to gravity at sea level and c is a constant What is the velocity of the ball as a nmction of time? 40. determine the position of thc ball relative to its initial position as a function of time. 44 If aerodynamic drag is taken into account, the acceleration of a falling object can be approximated by a = g - cJ, where g is the acceleration due to gravity at sea level and c is a constant.
Il , In some situations, lithe acceleration of an object is constant, or nearly constant. For example, if you drop a dense object such as a golf ball or rock and it doesn't fall too fh, you can neglect aerodynamic drag and asstune that its acceleration is equalll to the acceleration of gravity at sea level. 22 STRAIGHT-LINE MOTION Let the acceleration be a known constant ao. 12) where So and Vo are the position and velocity, respectively, at time to. Notice that if the acceleration is constant.