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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.

Michael Mshtc
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3 Answers3

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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 $\sqrt{501}m/s$.

Crocogator
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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...

sidhartha
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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,

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

Quanto
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