Margy is trying to improve her cardio endurance by performing an exercise in which she alternates walking and running 100.0 m each. If Margy is walking at 1.4 m/s and accelerates at 0.20 m/s2 during one of the running portions, what is her final velocity at the end of the 100.0 m? Round your answer to the nearest tenth.

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- dan815

okay so

- dan815

she starts at 1.4 m/s
and accelerates 0.2 m/s^2 over a distance of 100.0m

- dan815

now okay lets suppose it takes t seconds for her to run this 100.0m while she is accelerating

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## More answers

- dan815

now the velocity over this time period will look like
v(t) = 1.4 + 0.2 *t <---- tells you the veloicty with respect to the time
the distance over this time will look like the area under this graph, as that will tell you how much distance is constantly being covered over this time,
now the area has to be = 100 in total, so wee see the time that takes and the final velocity

- greentravis

okay

- dan815

|dw:1444179878145:dw|

- dan815

|dw:1444179933274:dw|

- dan815

this is a trapezoid which can be broken down into a triangle and a rectangle, what is the area of this?

- dan815

or u can take the average height of this traepezoid and multiply by the width thats the same thing

- dan815

|dw:1444180009855:dw|

- greentravis

so the area would be 6.5 m/s right?

- dan815

no the area is 100 m the area is the distance since this is veloicty vs time graph
and veloicty * time = displacements or i guess distance here

- greentravis

okay

- dan815

this method is probably new to u... just ask me anything u want

- dan815

theres also jut a formula u can use, maybe that better for just now

- dan815

x(t) = Xi+Vi*t + 1/2at^2
Xi is the initial position taken to be 0 here
Vi is initial speed which is 1.4 m/s
a is 0.2 m/s^2
and you know total distance was 100
so
100= 0+1.4*t + 1/2 * 0.2 * t^2
solve for t
and then
use the fact that
v=1.4+0.2*t, to find the final velocity

- greentravis

i mean velocity

- dan815

velocity or speed same thing here, because this is one just 1 dimension and hes only moving forward so

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