# Math Help - Help with Initial Velocity Problem

1. ## Help with Initial Velocity Problem

When its brakes are applied, a certain automobile has constant deceleration of 22ft/s^2. If its initial velocity is 90 mi/h, how long will it take to come to a stop? How many feet will it travel during that time?

2. If deceleration is constant, than our velocity at any time can be calculated by subtracted a*t from our initial velocity.

V = Vi - at

Now if you integrate you get a formula for distance, and your + C we'll just consider as 0.

3. Originally Posted by derfleurer
If deceleration is constant, than our velocity at any time can be calculated by subtracted a*t from our initial velocity.

V = Vi - at

Now if you integrate you get a formula for distance, and your + C we'll just consider as 0.
if acceleration is 22ft/s

then the formula for acceleration is

$g=-22$

now you need to find the velocity formula

where that is the anti derivative of acceleration

$v(t)=-22t+90$

where t is time in seconds and 90 is the inital velocity which in this case C

to show my work

$90=-22(0)+C$
$C=90$

It will have stopped when velocity is 0

so $v(t)=-22t+90$ = 0 and solve for t
$0=-22t+90$
$-90=-22t$
$90/22=t$

t = 4.09

no you need to find the distance traveled for this time now you must take the anti derivative of the velocity formula which is

$s(t)=-11t^2+90t+C$

C is in the distance formula for something like this is 0 because C or s(t) sub 0 is usually initial height

so now plug in

t = 4.09

$s(4.09)=-11(4.09)^2+90(4.09)$

which equals 184.0909 feet

I maybe be totally wrong here
but it takes 4.09 seconds to stop and the car travels a distance of 184.09 feet

4. What're you quoting me for? =p

By the way, ft/s doesn't transfer over too well into mph. =p

5. Originally Posted by derfleurer
What're you quoting me for? =p

By the way, ft/s doesn't transfer over too well into mph. =p
just instinct since im usually asking for help

ohh yeahhh dont really know how to do the conversion however is that right?

but the problem did ask how many feet it traveled

6. If your acceleration is in ft/s/s, than when you integrate, your velocity is in terms of ft/s. Meaning your constant of integration cannot be in mi/h.

Substitute 132ft/s for 90m/h. And do your time and distance calculations again. Everything else you did was right.

7. Oh yes that is true thanks for pointing that out