Choosing the Appropriate Kinematics Equation

Physics Tutorial

Choosing the Appropriate Kinematics Equation


In the study of motion in physics, there are five kinematics equations that can be used to solve problems involving constant acceleration. They are:

V = Vo + at
d = 1/2*(Vo + V)*t
d = Vo*t + 1/2*at^2
d = V*t – 1/2*at^2
V^2 = Vo^2 + 2ad

Notice that each equation contains exactly four of the five kinematics variables (Distance d, Initial velocity Vo, Final velocity V, Acceleration a, and Time t). The first equation is missing d, the second equation is missing a, the third equation is missing V, the fourth equation is missing Vo, and the fifth equation is missing t.

Students often have a hard time deciding which equation to choose for solving a problem, so this sample problem will show how to choose the appropriate equation and solve the problem.

Sample Problem

An airplane, starting from rest, accelerates at 4 m/s^2 to a speed of 100 m/s, which is required for takeoff. What length of runway is necessary?


First, identify three variables that are known and write them down, and identify the variable you are asked to solve for, and write it down with a question mark. For this problem, we have:

Vo = 0 (since the airplane starts from rest)
a = 4 m/s^2
V = 100 m/s
d = ?

Since d is unknown, students often make the mistake of trying to use the kinematics equation that is missing d. However, the equation should be chosen based on the variable that is completely missing from the above list, which in this case is t. We don’t know what t is, and we’re not asked to find t. Looking at the list of kinematics equations, it is the fifth equation that is missing t, so we’ll use that one.

Start by writing down the equation:

V^2 = Vo^2 + 2ad

If any variable in the equation is zero, remove it. In this case, Vo = 0:

V^2 = 2ad

Rearrange the equation to get the unknown variable by itself. In this case, we are solving for d, so divide both sides by 2a:

V^2/2a = d

Finally, plug the numbers in:

d = 100^2 / (2*4) = 10,000 / 8 = 1250 m or 1.25 km

About The Author

Top Quality Tutoring For All Levels Of Math, Physi
Get extremely effective tutoring from a skilled educator with two master’s degrees and 20 years experience at the middle school, high school, and university level. I have taught Geometry and Algebra I & II classes with a 100% SOL pass rate. I have also taught AP Calculus (AB & BC), AP Physics (...
22 Subjects
KnowRo Tutor
1 Tutorial
Richmond, VA
Get Tutoring Info

Suggested Tutors for Physics Help

Brent A

Seabrook, NH

Chemistry And Physics

Altai P

Durham, NH

Science And Math Tutor

Paul P

Dover, NH

Math Subject Matter Expert And SAT Instructor

Salme C

Dover, NH

Engineer With Teaching/Tutoring Experience