Question

While you are sitting on a park bench with your friend, you grab his hat and start running in a straight line away from him. Over the first 50m, you accelerate at 1.00m/s^2 up to your maximum running speed. You then continue at you maximum running speed for 5s more before your friend catches you. How far from the bench did you get before being caught?

Answer 1

Strategy:
1) Find distance traveled when he accelerate.
2) Find distance traveled when he run with constant speed.

Answer 2

1) x=v0t+1/2 * at^2
2) x=v*t

Answer 3

ok , let me quickly try that out!

Answer 4

the initial velocity is 0?

Answer 5

Yep, he was sitting back then

Answer 6

d= 0 + 1/2 (1m/s^2) t
what do i do for the time?
the question says 1m/s^2 to his max acce, but i dont know what is his maximum acceleration

Answer 7

Heheh, actually, you can use v^2=v0^2+2ax to find v, (no need to use eq (1) then).

Answer 8

then x= 50m?

Answer 9

but arent u trying to find x? (How far from the bench did you get before being caught? )

Answer 10

You already find x for first part (50 m). And we can use this x to vind his max velocity

Answer 11

so he get caught at x=50..?

Answer 12

No, he caught after running 5 sec with max velocity beyond that 50 m.
So, find (2) first. He will be caught at distance 50 m + distance traveled at (2).

Answer 13

but how can i do it if i dont know the maximum velocity

Answer 14

x= v * t. i dont know both x and v

Answer 15

Use this v^2=v0^2+2ax

Answer 16

but i still dont know both x and v

Answer 17

if i'm solving for (2) first, that means i 'm not using 50m

Answer 18

x is 50 m here v0=0, and v is vmax you're looking for.

Answer 19

and with the vmax, i sub it in x= v*t to find the distance after 50m?

Answer 20

Yep, you're on it.

Answer 21

this thing is so confusing..how can u guys even get this ==..omg..

Answer 22

for the time, do i use d= v1 t + 1/2 a t ?

Answer 23

Which time do you mean?

Answer 24

How long did it take for your friend to catch you?

Answer 25

You already know the time at second part (5 s). Now find for the first.
Yes, you can use that for known a (1.00 m/s^2) and d (50 m).
Alternatively
v=v0+at (v and v0 also known)

Answer 26

so if i find t using v=v0+at , do i need to add it to that 5s too?

Answer 27

i got like over 100s, dont think that's right

Answer 28

i got the right ans..dont know how and why i get it..but sure..thanks !

Answer 29

Heheh, practice and you'll understand.