Driver sees stop sign up ahead

[unholymist]

Homework Statement

I am having some trouble with a question. Here it is:

David is driving along at 25m/s when he sees a stop sign ahead. He hits the breaks at 10m from the sign. He decelerates at 4m/s-squared. Does he stop in time?

Homework Equations

We were given the equations of motion. The question gives displacement, initial velocity, and acceleration.

The Attempt at a Solution

My main gripe with this question is that it doesn't give a time that he must reach. Is another car going to reach the traffic stop in 10 seconds? 15 seconds? It doesn't say...

I thought of simply seeing how long it would take him to reach it if instead of braking he kept going at constant velocity but no luck.

Can someone help me out?

 

[member 198005]

Ignore the time -- in this case it doesn't matter. The question only asks if he can completely stop in 10m. There just so happens to be a kinematic equation that doesn't contain time. Finding that equation makes this a (relatively) simple algebra problem.

 

[supratim1]

time is not asked. by 'does he stop in time' it is meant whether he stops within 10m distance.

 

[HallsofIvy]

You could calculate the time required to stop from the formula [math]v= -at+ v_0[/math], taking v= 0. Then use the distance formula x= -(a/2)t^2+ v_0t[/math] to determine whether he &quot;stopped in time&quot;- whether he stopped before going 10 m.<br /> <br /> By the way, he hit the &quot;brakes&quot;, not the &quot;breaks&quot;!

 

[unholymist]

You could calculate the time required to stop from the formula [math]v= -at+ v_0[/math], taking v= 0. Then use the distance formula x= -(a/2)t^2+ v_0t[/math] to determine whether he &quot;stopped in time&quot;- whether he stopped before going 10 m.<br /> <br /> By the way, he hit the &quot;brakes&quot;, not the &quot;breaks&quot;!

<br /> <br /> Hehehe yeah. I was in a hurry. &gt;.&lt; That&#039;s an embarrassing mistake. <br /> <br /> Thanks for the help everyone. Figured it out... don&#039;t how I didn&#039;t realize that right away.