# 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