Two people, Lesley and Jaime, are racing each other. Assume that both their accelerations are constant, Lesley covers the last 1/6 of the race in 3 seconds, and Jaime covers the last 1/3 of the race in 6 seconds. Who wins, and by how much?

Question

anonymous · Answer

Say, full race will cover distance $d$.
$$x=\frac12 at^2 \\frac16 d=\frac12 a_L3^2 \\frac13 d=\frac12 a_J 6^2 $$
From here you can find each acceleration of L and J (which seems J if faster tahn L).
After finding a, find t when J cover distance d:
$$d=\frac12 a_J t^2\t=... $$
Then find the distance traveled by L in that time:
$$x=\frac12 a_Lt^2$$
This will do i think. Any better solution?

anonymous · Answer

My textbook says To answer this question, we need a formula for the time it takes an object accelerating from rest at a constant acceleration a to travel a distance d. This formula is ...

anonymous · Answer

t=...

anonymous · Answer

$$d=\frac12 at^2\t=\sqrt{\frac{2d}{a}}$$

anonymous · Answer

Using this formula, we find that the time (in seconds) it takes Lesley to run the race is....

anonymous · Answer

What's your answer?

anonymous · Answer

I cant figure it out honestly

anonymous · Answer

I just found that for J :54a=d and for L : d=9a

anonymous · Answer

any ideas?

anonymous · Answer

Using this formula, we find that the time (in seconds) it takes Lesley to run the race is....
$$t=\sqrt{\frac{2d}{a_L}}$$ we can find Lesley's acceleration $a_L$ first if you want

anonymous · Answer

Lesley covers the last 1/6 of the race in 3 seconds.what is her a

anonymous · Answer

I am so damn confudsed

anonymous · Answer

Use $$d=\frac12 at^2$$

anonymous · Answer

Find a for known d and t

anonymous · Answer

d isnt known

anonymous · Answer

d is $\frac16$

anonymous · Answer

for t = 3 s

anonymous · Answer

it is 1/6 d

anonymous · Answer

Yeah you may use 1/6 L or 1/6 something or just 1/6. It'll give the same answer.

anonymous · Answer

1/6 d isn't recommended. you already choose d as symbol of distance traveled.

anonymous · Answer

Can you just solve the problem ;)

anonymous · Answer

Lol, @Algebraic! he's asking you.

anonymous · Answer

ok I am screwed

anonymous · Answer

Okay-okay, lets begin something called finding acceleration of both L & J. Can you find them?