In the introduction, the convservation of energy was one of the concepts that play into the interaction between the Flash and the wall, and now you will know why. If the Flash wanted to run up a wall, hd doesn't just start at the bottom and start running up. No, he runs horizontally, on the ground first, and then he puts a foot on the wall, pushes, then he puts his other foot on the wall and pushes, and the pattern repeats. He has built up kinetic energy, but once he starts moving up the building that Kinetic Energy is transformed to Gravitational Potential Energy, all the while the change in the energy of the system is zero.

In this picture you see first the Flash running on the ground and towards the wall, this is the beginning of conservation of energy. Then he is at the top of the building and he now has Gravitational Potential Energy, this is the end of the conservation of energy.

Assuming that it is possible to run up a a building, we need to find the speed that is required for him to run up a building. I arbitrarily chose an 8-story building for this equation. 8 stories is approximately 24 meters tall (converstion: 1 story = 3 meters) The conservation of energy is mathematicaly represented as Ugi + KEi = Ugf + KEf

In the beginning there is no Ugi because the Flash is at ground level. At the end there is Ugf but no KEf because he is above ground level and are no longer moving.

Therefore, the equation for energy for this system is KEi = Ugf

Using the equations for KE and Ug, the equation is ½ ×m × vi2 = m × g × d



After some algebra, the equation for velocity is vi = √ 2×g×d 
You'll notice that the masses cancel out which makes sense because the Flash is the Flash at the beginning as well as at the end.

With g = 9.8 and d = 2, you'll find the equation is now vi = √ 2×(9.8)×(24)  = 21.68 meters/seconds . That is equivalent to 70 feet per second! That is just to run up an 8-story building. Just think, the Flash has to run up 20-story buildings or more. Thinking in terms of the average human, according to LivingIt the average person's running speed is in the range of 10 to 15 mph. Converting that to feet/seconds: that is from 14.66 to 22.

LivingIt also noted that the highest speed that a human can theoreticaly run is 45 km/h which is equivalent to 41 feet/seconds. That means in order to run up an 8-story building an average person would have to run 5 to 3 times faster, and the fastest person in the world would have to run barely less than 2 times faster.

In conlusion, it is not possible for the average human to run fast enough to run up an 8-story building. Thank goodness, the Flash is superhuman.

Now, to find out if the physics say that the Flash can run up a buliding click on the Is It Possible? tab.