Motion Problem Help: Should She Stop or Go?

[Gughanath]

A person driving her car at 56 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning to red, and she is 30 m away from the near side of the intersection (Fig. 2-29). Should she try to stop, or should she make a run for it? The intersection is 15 m wide. Her car's maximum deceleration is -7.0 m/s2, whereas it can accelerate from 56 km/h to 70 km/h in 4.2 s. Ignore the length of her car and her reaction time.

If she hits the gas instead, how far will she travel before the light turns red?

I think there is not enough details given in the question to solve this problem? Is there a way to do this?

 

[whozum]

Crunch some numbers, its doable. You know her max acceleration and braking time. See if she can make it through or not.

 

[Gughanath]

I don't know her a max acceleration. That is the problem. The question only gives me the deceleration.

 

[tony873004]

I don't know her a max acceleration. That is the problem. The question only gives me the deceleration.

You can compute her max acceleration with
"whereas it can accelerate from 56 km/h to 70 km/h in 4.2 s"

I think they threw in an irrelavant piece of data with the 15 meters wide, unless traffic laws in her state are different from California. Here, you only need to be in the intersection when the light turns red, and not all the way through.

The only "not enough info given" part is it doesn't say that if she accelerates that she will floor the gas, so although you can compute her max acceleration, she may only need a modest amount of acceleration to make it through, and if she's not a lead foot she won't floor it. So without knowing her actual acceleration, you can't compute how far she will travel before the light turns red.

 

[Gughanath]

But not knowing her final velocity, I can't work out the acceleration, can I?

 

[tony873004]

But not knowing her final velocity, I can't work out the acceleration, can I?

Sure. You're computing an average acceleration. Your initial velocity is 56 km/h, and your final velocity is 70 km/h. It takes the car 4.2 seconds to change velocity from 56 to 70.

First, you need to be in MKS. So convert your velocities to meters/seconds:
$$v_i =\frac{56\rlap{--} {k}\rlap{--} {m}/\rlap{--} {h}\rlap{--} <br /> {r}}{3600s/\rlap{--} {h}\rlap{--} {r}}\cdot \frac{1000m}{\rlap{--} <br /> {k}\rlap{--} {m}}=15.555m/s$$

Do the same for your final velocity

Your formula for change in velocity is
$$\]<br /> \[<br /> \Delta v=\left| {v_f -v_i } \right|<br /> \]<br /> \[$$

And your formula for computing average acceleration is
$$a_{avg} =\frac{\Delta v}{t}$$

 

[Gughanath]

Thanks. Problem Solved:D