$\begingroup$

The problem is as follows:

A car is going at initial velocity 1 m/s when a brick wall appears 50 m away. Assuming the driver reacts instantaneously and accelerates at a constant rate of 5 $m/s^2$, at what speed will the driver hit the brick wall?

I tried using the formula of $$d=Vt+1/2at^2$$ and tried to isolate for time with algebraic manipulations but the farthest I get is to $$t=d/(V+1/2at)$$ How to solve for time? With time I can find final velocity using equation Final Velocity = Initial Velocity + Acceleration * Time.

I could not find the answer in any other questions.

asked Sep 21 '17 at 2:08

$\endgroup$

8

  • $\begingroup$ Hint: $$2 a d = v_f^2 - v_i^2.$$ $\endgroup$

    Sep 21 '17 at 2:25

  • $\begingroup$ @Sou this is a perfect question for math.SE in Physics.SE they will not answer this type of questions. This is just related to mathematics and solving an equation $\endgroup$

    Sep 21 '17 at 3:25

  • $\begingroup$ Are you sure that the initial velocity is 1m/s ? The driver accelerates or decelerates the car? $\endgroup$

    Sep 21 '17 at 3:34

  • $\begingroup$ @ Rafael Wagner All right. I'm sorry if i'm not familliar with the rules. That just my opinion. $\endgroup$

    Sep 21 '17 at 9:37

  • $\begingroup$ @Sou And did your opinion change after Rafael's explanations? $\endgroup$

    Sep 21 '17 at 15:44

3 Answers 3

$\begingroup$

Here you only need a single formula that is,

$v^2-u^2=2as$

Where, v = final velocity, we have to find it u = initial velocity, 1m/s a = acceleration, 50m/s^2 s = distance, 50m

Putting the values,

$v^2-1^2=2×50×50$

$v^2=500+1$

$v=\sqrt{501}$

Hence the vehicle will hit the wall at $\sqrt{501}m/s$.

answered Oct 12 '19 at 2:42

$\endgroup$

$\begingroup$

If the question is saying that car accelerates then you can find time by simply substituting the given values in equation., but if it is decelerating you don't get an answer for time...

answered Sep 21 '17 at 6:18

$\endgroup$

$\begingroup$

You need two following equations to find the final speed $V_f$,

$$d=V_i t+\frac 12at^2$$ $$V_f-V_i = a t$$

Combine the two to eliminate the time $t$ and you will get,

$$V_f^2=V_i^2+2ad$$

answered Oct 11 '19 at 21:28

$\endgroup$

Not the answer you're looking for? Browse other questions tagged physics or ask your own question.