A negative instantaneous acceleration means the velocity is decreasing. If it is positive, our velocity is increasing. Using Calculus to Find Acceleration Acceleration is measured as the change in velocity over
In calculus we use the terms instantaneous acceleration and instantaneous velocity to talk about very accurate measurements of acceleration and velocity. Acceleration is still defined as the rate of change of velocity, but these measurements refer to motion at an instant instead of over a period of ...
During his study of pendulums, Huygens discovered that a ball rolling back and forth on an inverted cycloid completes a full “swing” in exactly the same amount of time. He solved the tautochrone problem without calculus, usingEuclidean geometry[4]. In addition to the cycloid, there are an...
To be mathematically rigorous, we would need to determine the equation of the parabolic curve and then use some calculus to determine the slope of the curve at every point in time. However, we can make some assumptions to simplify our scenario. We know that our parab...
…I began to honestly enjoy learning all the new applications for the calculus concepts I had been learning alongside physics, previously unaware of just how intertwined they were. The relationship between position, velocity, and acceleration through derivatives and integrals tied everything together in...
The big problem is to find such an angel and this article will tell how and where to find angels. Many years ago a small business could start a company, enlist the aid of a broker-dealer, and file to sell shares in a risky venture. All start-up companies are risky. Shares could be...
If you’d like to find out why in the example above the ball ended up traveling at 0.88c instead of something else, or what would happen if Walter “The Big Train” Johnson had thrown the ball sideways off of the train, you’ll find i...
The Calculus of Uniform Circular Motion Learning Goal: To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle is traveling around a circl To...
Find the maximum height the ball reaches. David throws a ball straight upward from the ground with an initial velocity of 320 ft/sec. What is the maximum height the ball will reach? Use Calculus. A ball is thrown upward ...
II. The velocity of the motion being continually given; to find the length of the Space describ’d at any time propos’d (Whiteside, p. 50). References Kitcher, P. Fluxions, Limits, and Infinite Littlenesse: A Study of Newton’s Presentation of the Calculus. Isis. Vol. 64, No. 1...