Calculate velocity of stopping car

[Lizi]

Homework Statement

A car moving at 20m/s starts decelerating, travels distance d, and stops. Find the car’s velocity at distance d/2.

Homework Equations

The Attempt at a Solution

my brain is fried. I feel like I’m missing something obvious but I just don’t get it.

 

[stockzahn]

I suppose you should assume a constant deceleration

 

[neilparker62]

Homework Statement

A car moving at 20m/s starts decelerating, travels distance d, and stops. Find the car’s velocity at distance d/2.

Homework Equations

The Attempt at a Solution

my brain is fried. I feel like I’m missing something obvious but I just don’t get it.

It was a bit of a brain 'fry' !

Time 'reversing' so that we have acceleration from 0 m/s instead of deceleration from 20 m/s:

$$ d = ½at^2 ⇒ \frac{d}{2} = ½a\left({\frac{t}{\sqrt{2}}}\right)^2 ⇒v=\frac{at}{\sqrt{2}}$$

 

[stockzahn]

It was a bit of a brain 'fry' !

Time 'reversing' so that we have acceleration from 0 m/s instead of deceleration from 20 m/s:

$$ d = ½at^2 ⇒ \frac{d}{2} = ½a\left({\frac{t}{\sqrt{2}}}\right)^2 ⇒v=\frac{at}{\sqrt{2}}$$

But since you don't know $a$ you can't obtain $t$, so you stick with two unknowns. I think the question should be solved independent of the time ...

 

[CWatters]

Edit: This cross posted with some of the above;

It gives you the initial velocity (u) and asks you to find the cars velocity (v) after traveling a distance (s = d/2). What equation relates u,v,s and a?

You aren't given the acceleration (a) but you can work it out from the first part of the problem statement.

 

[neilparker62]

But since you don't know $a$ you can't obtain $t$, so you stick with two unknowns. I think the question should be solved independent of the time ...

at = ?

 

[stockzahn]

at = ?

Still, I think the medthod @CWatters proposes is the preferred one. Additionally it should be the OP's task to solve it ...

 

[Lizi]

guys, I figured it out using the d=(v²-u²)/(2a) formula.
Thank you all so much