Kinemetics Question - theoretical subsitution

[Pardicer]

Homework Statement

This is for personal study and as I am on study leave its a bit hard to contact a teacher.

This is the question; (the circled answer was the teachers answer)

I'm unsure as to why you would individually square the times before subtracting as the actual time is (t2-t1) substituted into time on the equation, squaring before will result in a larger value (small value for acceleration though). It is possible the teacher merely got it wrong (has been known to happen).

Homework Equations

s=ut + (1/2)at^2

The Attempt at a Solution

 

[SammyS]

Your equation,  h = 0(t₂-t₁) + (1/2)a(t₂-t₁)²  is in error.

The velocity, u₁, at time, t₁ is not zero. This velocity is give by:

u₁ = u₀ + a(t₁-t₀) = 0 + a t₁ = a t₁ .​

∴ h = u₁(t₂-t₁) + (1/2)a(t₂-t₁)²

= (a t₁)(t₂-t₁) + (1/2)a(t₂-t₁)²​

If you multiply this all out, combine like terms and then factor it, you will find that your teacher did indeed give the correct answer.

BTW: There is an easier way to come up with his answer. I thought it better to use what you started with.