1D Kinematics Legacy Problem #18 Guided Solution

This problem, like many in this problem set, involves the use of the kinematic equations. The basic idea of the kinematic equations is that we can calculate how fast something will be moving, or how far it will go, or what time it will take to get there, if we know three bits of information about an object's motion. Because within each of the kinematic equations are four variables, thus, knowing three, we can calculate a fourth. In this problem, what we know is the takeoff speed of a Cessna 150 airplane is 28 meters per second. Now, if you think about an airplane, it sits on the runway, it gets signaled from control tower, and it takes off from rest. So we know the initial speed at which it begins to accelerate along the runway, and the final takeoff speed. It goes from zero meters per second to 28 meters per second, accelerating along the way at a rate of 1.9 meters per second per second. So there are the three bits of information that you will need to know in order to calculate the unknown quantity, the distance it travels along the runway. And so you're going to now look for an equation that has the four variables in it, the D, which we're looking for, the original zero, the V final at 28 meters per second, and the acceleration at 1.9 meters per second per second. Once you find that equation, take your three known values and substitute it into it, and solve for the fourth. The equation is the one that is listed on the overview page as VF squared equals VO squared plus 2AD. Substituting and solving will get you an answer of about 206 point something, and if you round it to two significant figures, you'd have 210 meters.