![]() We recommend using aĪuthors: William Moebs, Samuel J. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the From the functional form of the acceleration we can solve Equation 3.18 to get v( t):.We take t = 0 to be the time when the boat starts to accelerate opposite to the motion. (d) Since the initial position is taken to be zero, we only have to evaluate the position function at the time when the velocity is zero. (c) Similarly, we must integrate to find the position function and use initial conditions to find the constant of integration. (b) We set the velocity function equal to zero and solve for t. Strategy(a) To get the velocity function we must integrate and use initial conditions to find the constant of integration. (a) What is the velocity function of the motorboat? (b) At what time does the velocity reach zero? (c) What is the position function of the motorboat? (d) What is the displacement of the motorboat from the time it begins to accelerate opposite to the motion to when the velocity is zero? (e) Graph the velocity and position functions. Its acceleration is a ( t ) = − 1 4 t m/ s 3 a ( t ) = − 1 4 t m/ s 3. Motion of a MotorboatA motorboat is traveling at a constant velocity of 5.0 m/s when it starts to accelerate opposite to the motion to arrive at the dock. Since the time derivative of the velocity function is acceleration, Let’s begin with a particle with an acceleration a(t) which is a known function of time. Kinematic Equations from Integral Calculus Using integral calculus, we can work backward and calculate the velocity function from the acceleration function, and the position function from the velocity function. By taking the derivative of the position function we found the velocity function, and likewise by taking the derivative of the velocity function we found the acceleration function. In Instantaneous Velocity and Speed and Average and Instantaneous Acceleration we introduced the kinematic functions of velocity and acceleration using the derivative. This section assumes you have enough background in calculus to be familiar with integration. ![]()
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