Please help me out. :(

A car moving at a constant velocity of 14 m/s passes a gasoline station. Two seconds later, another car leaves the gasoline station and accelerates at the constant rate of 2 m/s^2. How soon will the second car overtake the first?

Question

Please help me out. :(

A car moving at a constant velocity of 14 m/s passes a gasoline station. Two seconds later, another car leaves the gasoline station and accelerates at the constant rate of 2 m/s^2. How soon will the second car overtake the first?

anonymous · Answer

my answer is 11.583 s and 2.417 s.
is it correct?

ganeshie8 · Answer

show your work also so that others can avoid duplicating your effort :)

anonymous · Answer

okay. :)

anonymous · Answer

denotation:
1st Car = Honda
2nd Car = Toyota

Given:
dT = 2 m/s^2
vH = 14 m/s
tT = tH - 2


dT = dH
1/2 at^2 = vt
tT = 11.583 seconds
tT = 2.417 seconds


tT = tH - 2
tH = 13.583 seconds
tH = 4.417 seconds


ANSWER: tT = 11.583 seconds and 2.417 seconds

ganeshie8 · Answer

very nice try :)

ganeshie8 · Answer

2 m/s^2

this is the acceleration of second car right ? (Toyota)

anonymous · Answer

yes.. that's it..

ganeshie8 · Answer

So position equations for the cars can be given like below :

First car(Hyundai) :  
$$\large   S_h =  14t$$

Second car(Toyota) :  
$$\large   S_T =  \dfrac{1}{2}2(t-2)^2 =   (t-2)^2$$

ganeshie8 · Answer

When the second car overtakes the first car,
the position of both cars would be same

ganeshie8 · Answer

So simply set both equations equal to eachother and solve $\large  t$

ganeshie8 · Answer

$$\large   S_h =  S_T   $$

$$\large   14t =  (t-2)^2   $$

ganeshie8 · Answer

Solve $\large t$

anonymous · Answer

i got two answers on that...

ganeshie8 · Answer

only one answer makes sense,
throw away the other one

ganeshie8 · Answer

Considering the fact that the second car has started "2" seconds after the first car, which answer is invalid ?

anonymous · Answer

0.225 s.

ganeshie8 · Answer

yes thats the one you need to throw away, whats the correct answer and what does that represent exactly ?

anonymous · Answer

17.775 s. :)

ganeshie8 · Answer

thats right ! what does 17.775s represent ?

ganeshie8 · Answer

is it the time after First car 
or the time after Second car ?

anonymous · Answer

time after 2nd car..

ganeshie8 · Answer

nope

ganeshie8 · Answer

we have defined "t" as the time after the first car has started, right ?

ganeshie8 · Answer

So  17.775s corresponds to the time after the first car

anonymous · Answer

ahh.. okay.. im wrong. huhu

ganeshie8 · Answer

basically the Second car overtakes the First car exactly after  17.775s the First car starts


So the first car travels for 17.7755s
and the second car travels for 15.7755s before overtaking

anonymous · Answer

ahh.. so, what's the final answer?