# Working With 1D Constant Acceleration Kinematics

Hello, this is my first post on PhysicsForums. I'm a first year student at the University of Kansas pursuing a Bachelor of Science in Physics and Astronomy (double majoring). The wording on my homework (for Honors General Physics 1) is a little bit strange to me so maybe some of you guys and girls can help me iron it out. Thanks in advance!

1. Homework Statement

Draw a graph of velocity versus time of an object starting with a velocity v0 and increasing speed with a constant acceleration(this is easy and not a problem). We know that v-v0=∫vdt (this is also quite obvious and easy to deduct), so the displacement is the area under the plot you just drew(simple integration). Show that for this case (constant acceleration): vave=1/2(v0+v) - (although I know this is true, I don't exactly know how to "show" it?), and then, by equating this result with the definition of vave and eliminating t(this is ultimately what hangs me up. I have no idea how to eliminate t. I know that the definition of vave) = Δx/Δt but I am not sure how to rid the equation of time), v2=v02+2aΔx

v2=v02+2aΔx
vave) = Δx/Δt
ave=1/2(v0+v)

## The Attempt at a Solution

Since this is more of a conceptual approach to understanding this idea, I have very little work done for this specific problem. I have finished the other two problems in the question set though (total of 3 problems).

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haruspex