Working With 1D Constant Acceleration Kinematics

[Entangled Cat]

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): v_ave=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 v_ave and eliminating t(this is ultimately what hangs me up. I have no idea how to eliminate t. I know that the definition of v_ave) = Δx/Δt but I am not sure how to rid the equation of time), v²=v_0²+2aΔx

Homework Equations

v²=v_0²+2aΔx
v_ave) = 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).

 

[haruspex]

v-v0=∫vdt

s-s₀?

v_ave=1/2(v₀+v)

This is just geometry. What shape have you drawn? How would you find its area?

and eliminating t

There seems to be something missing here in the instructions. To eliminate t you need two equations involving t. The other equation you need is the definition of acceleration.