# Thread: Transposition and subsitituion, or differentiation?

1. ## Transposition and subsitituion, or differentiation?

Given that s=ut+1/2 at^2 and that the rate of change of distance with time =speed show that v=u+at

I'm not sure where to begin with this question, I did two other which were similar and they were just transposition and substitution, But this looks like its aking for me to prove the derivative, Am i completely off base or just thick?

Any help is apprecciated!

Ally

2. Originally Posted by ally79
Given that s=ut+1/2 at^2 and that the rate of change of distance with time =speed show that v=u+at

I'm not sure where to begin with this question, I did two other which were similar and they were just transposition and substitution, But this looks like its aking for me to prove the derivative, Am i completely off base or just thick?

Any help is apprecciated!

Ally
start with $s = ut + \frac 12at^2$

and differentiate both sides with respect to $t$. the result follows

3. where did the a go?

4. Originally Posted by ally79
where did the a go?
i forgot it.

i changed it

thanks

5. i see when i differentiate ut+1/2at i get u+at i dont see how differentiating S gives me V?

6. V is the rate of change of S w/r to time.