Question

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?

Answer 1

If we could find their acceleration, then we can find the time it takes for them to finish the race.
@vancouver2012 how would relate distance with acceleration and time?

Answer 2

derivatrive

Answer 3

\[S=ut+\frac 12 at^2\]
Do you know this equation?

Answer 4

in physics yea

Answer 5

I'm thinking, how we'd use this.

Answer 6

t=sqrt(2*d/a)

Answer 7

Initial velocity=0 for the starting of the race not for the scenario we are given

Answer 8

the answer key says use t=sqrt(2*d/a)

Answer 9

its given as a hint

Answer 10

Lesley covers the last 1/6 of the race in 3 seconds
let the race length be x so
\[\frac {x}{6}=u1 \times 3+\frac 12 a (3)^2\]
u1= initial velocity of Lesley for the last 1/6 of the race
Similarly for Jaime, we write this equation
\[\frac {x}{3}=u2 \times 6+\frac 12 a (6)^2\]
also
\[v^2-u^2=2as\]
for lesley
\[(u1)^2=2a \times \frac56 x\]
for Jaime
\[(u2)^2=2\times \frac 2 3 x\]
do you get this ?

Answer 11

not this v 2 −u 2 =2as

Answer 12

also this question is listed in derivative section

Answer 13

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

Answer 14

that is what the hint says after providing the formula that I provided

Answer 15

for Leslie
v=u1
u=0