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Determine the relation between elapsed time and distance traveled when a moving object is under the constant acceleration of gravity.
21 Νοε 2023 · Constant acceleration is an even more specific type of accelerated motion. An object that travels with constant acceleration has a speed that changes by the same amount each second.
We say that an object is “accelerating” if its velocity is not constant. As we will see in later chapters, objects that fall near the surface of the Earth experience a constant acceleration (their velocity changes at a constant rate). Formally, we define acceleration as the rate of change of velocity.
If the acceleration vector a is constant, we can bring it outside the integral sign of Eq. (11.1.4) just as we do with constant scalars. We get \[\mathbf{v}(t)=\int \mathbf{a} d t=\mathbf{a} \int d t\] or \[\mathbf{v}(t)=\mathbf{a} t+\mathbf{C}\] where \(\mathbf{C}\) is the constant of integration.
The definitions of velocity and acceleration we've seen so far ( \(v=d x / d t, a=d v / d t)\) are always true. But now let's look at an important special case: constant acceleration. First, assume that the acceleration \(a\) is a constant. Then by Eq. , \[\begin{align} v(t) & =\int a d t \\[6pt] & =a \int d t \\[6pt] & =a t+C, \end{align} \]
Motion with Constant Acceleration. Equations of motion relate the displacement of an object to its velocity, acceleration and time. The motion of an object can follow many different paths. Here we will focus on motion in a straight line (one dimension).
Learning Objectives. By the end of this section, you will be able to: Identify which equations of motion are to be used to solve for unknowns. Use appropriate equations of motion to solve a two-body pursuit problem.
