# Solve for time given distance and acceleration and initial velocity

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.

• Hint: $$2 a d = v_f^2 - v_i^2.$$ – Math Lover Sep 21 '17 at 2:25
• @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 – Rafael Wagner Sep 21 '17 at 3:25
• Are you sure that the initial velocity is 1m/s ? The driver accelerates or decelerates the car? – Rafael Wagner Sep 21 '17 at 3:34
• @ Rafael Wagner All right. I'm sorry if i'm not familliar with the rules. That just my opinion. – Sou Sep 21 '17 at 9:37
• @Sou And did your opinion change after Rafael's explanations? – Did Sep 21 '17 at 15:44

## 1 Answer

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...