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I'm not sure I understand what to do with what's given to me to solve this. I know it has to do with the relationship between velocity, acceleration and time.

At a distance of 45m from a traffic light, a car traveling 15 m/sec is brought to a stop at a constant deceleration.

a. What is the value of deceleration?

b. How far has the car moved when its speed has been reduced to 3m/sec?

c. How many seconds would the car take to come to a full stop?

Can somebody give me some hints as to where I should start? All I know from reading this is that $v_0=15m$, and I have no idea what to do with the 45m distance. I can't tell if it starts to slow down when it gets to 45m from the light, or stops 45m from the light.


Edit:

I do know that since accelleration is the change in velocity over a change in time, $V(t)=\int a\ dt=at+C$, where $C=v_0$. Also, $S(t)=\int v_{0}+at\ dt=s_0+v_0t+\frac{1}{2}at^2$. But I don't see a time variable to plug in to get the answers I need... or am I missing something?

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2 Answers 2

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Hint: Constant acceleration means that the velocity $v(t)=v(0)+at$ where $a$ is the acceleration. The position is then $s(t)=s(0)+v(0)t+\frac 12 at^2$. You should be able to use these to answer the questions.

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I wasn't thinking properly when I labeled this question as physics. Yes, it's a physics type question, but this is a calculus class, and I'm asked to do this as an exercise in integration. I do know though, that since accelleration is the change in velocity over a change in time, so $\int a\ dt = at+c$, where $c=v_{0}$. Also, $\int v_{0}+at\ dt = s_{0} + v_{0}t + \frac{at^{2}}{2}$. But I don't see a time variable to plug in to get the answers I need... or am I missing something? –  agent154 Jan 24 '13 at 18:33
    
@agent154: To find the time when the velocity is zero, use the velocity equation. Set $v(t)=0$ to get $t=\frac {-v_0}a$, then put this into the $s$ equation. You want $s(t)=45$, which will let you find $a,t$ –  Ross Millikan Jan 24 '13 at 18:45

The question is poorly formulated, but I imagine the intention is that the car is 45m from the traffic light and moving directly toward the traffic light when it begins to decelerate, and that it decelerates just enough to stop exactly at the traffic light. That seems to be enough information to lead to a unique solution, using what you already know.

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Indeed, that did help. I wouldn't be surprised if that's what the professor meant, seeing as he's foreign. Thanks for the insight. –  agent154 Jan 24 '13 at 19:14

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