# Kinematics Problem Solving

And that's what these equations are like, they're tools that we can use when we understand where they come from.

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We don't know what it is yet, but this is our question, we're being asked about the time.

All right, so if we keep going here, we get, all right, how long does it take to reach its top speed of 80 kilometers per hour? And then if we keep going, it says, "Starting from rest." So that's saying that at the beginning when it starts, it's at rest, which means it has zero for it's initial velocity, it's just sitting there.

Velocity is given by the straight line on the graph, and the position at time Example: A ball is thrown straight up with speed of 13.0 m/s from the top of a 40.0 m tall building.

(a) How high above the building's rooftop does the ball rise?

These problems may not be groundbreaking advances in modern physics, but they do represent very tangible everyday experiences: cars on roads, balls thrown in the air, hockey pucks on ice, and countless more examples can be modeled with these three relatively simple equations.

The first gives the change in velocity under a constant acceleration given a change in time, the second gives the change in position under a constant acceleration given a change in time, and the third gives the change in velocity under a constant acceleration given a change in distance.We do not know why the velocity is constant; we do not know why the acceleration has a given value. Usually only two types of motions are considered in kinematics problems: Motion with variable acceleration is quite complicated.Only in some special cases can we easily solve such problems, but usually we need to solve second order differential equations to get the answer in these problems.It's important to know how to add, subtract, to multiply and divide, so you know what a calculator is doing when you use it.But once you understand that, the calculator is a really valuable tool.Another difficult part in kinematic problems is related to the description of relative motion.The equations of 1D Kinematics are very useful in many situations.All of the equations of motion in kinematics problems are expressed in terms of vectors or coordinates of vectors.This is the most difficult part in kinematics problems: how to express the initial values or the final values in terms of the variables in the kinematic equations. We either know the velocity or acceleration, or the dependence of velocity on time or acceleration on time, but we need to find something else about this motion.For example, we know that the velocity is 30 mph during 5 hours and 50 mph during 1 hour and we need to know the traveled distance. In Kinematics we just need to find the parameters of the motion relation between velocity, acceleration, and distance.

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