# Solving Acceleration Problems

Again, solve for c by using the initial position condition. Given the position function, you can solve for the position of an object given the time t. Let’s do a slightly harder problem that involves position velocity and acceleration. I have no information about position but I could make the position function; s(t), be the position relative to the starting point, meaning that when t equals 0, s is 0. This course is an introduction to the study of bodies in motion as applied to engineering systems and structures.

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Before I figure out how to solve this problem, let me just write down the information that I’m given.

The fact that the acceleration is constant is really important. And acceleration is also the derivative of velocity.

So a car that is slowing by 4mph every second has an acceleration of -4mph/sec If we drop any object, it falls to the ground at a speed that is continuously increasing. It turns out that on Earth, this acceleration is approximately 32 feet per second every second (regardless of the object's weight, to the surprise of many).

So any object falling freely under the influence of Earth gravity accelerates at the rate of 32 feet per second every second.

So, to find the position function of an object given the acceleration function, you'll need to solve two differential equations and be given two initial conditions, velocity and position.

Since a(t)=v'(t), find v(t) by integrating a(t) with respect to t. That tells me that my velocity function is actually k times t. Now let’s take this and write it as a differential equation because v(t) is the same as s'(t).

When we check the speed one second later, we find the speed is now 32 mph.

So in that one second, the speed increased by 2 mph.

--------------------------- Suggested Readings: While no specific textbook is required, this course is designed to be compatible with any standard engineering dynamics textbook.

You will find a book like this useful as a reference and for completing additional practice problems to enhance your learning of the material.