If a single constant force acts on an object that moves on a straight line, the object’s velocity is a linear function of time. The equation v = vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi − kx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object.

A boxer's fist and glove have a mass of m = 1.04 kg. The boxer's fist can obtain a speed of v = 9.25 m/s in a time of t = 0.21 s. Write a symbolic expression for the magnitude of the average acceleration, aave, of the boxer's fist, in terms of the variables provided.  Find the magnitude of the average acceleration, aave, in meters per square second. Write an expression for the magnitude of the average net force, Fb, that the boxer must apply to his fist to achieve the given velocity. (Write the expression in terms of m, v and t.) What is the numerical value of Fb, in newtons?

A car is moving at 18.00[m/s], and comes to a stop in 3.45[s], due to friction acting on the car. Assuming the acceleration is constant, what is the magnitude of the acceleration experienced by the car? Express your answer in m/s2.

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PROBLEM: A ball with mass 0.15 kg is thrown upward with initial velocity velocity 20 m/s from the roof of a building 30 m high. Neglect air resistance.   Assume that the conditions are the same as the above except that there is a force due to air resistance of magnitude |v| / 30  directed opposite to the velocity, where the velocity v is measured in m/s. a. Find the maximum height above the ground that the ball reaches. b. Find the time that the ball hits the ground.  c. Plot the graphs of velocity and position versus time.  *** If possible, please solve for part b using the graphing calculator?  Thank you.

A pilot flew his​ single-engine airplane 60 miles with the wind from City A to above City B. He then turned around and flew back to City A against the wind. If the wind was a constant 20 miles per​ hour, and the total time going and returning was 1.3 ​hours, find the speed of the plane in still air.