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.
Best Answer
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 $\sqrt{501}m/s$.