[Math] Finding final velocity when initial velocity, distance travelled and acceleration are known

calculus

I've been struggling with this, I need to find the final velocity of a car after it travels a certain distance when I know it's initial velocity and acceleration are known. Any help?

Best Answer

Here's a way forward.

Motion under constant acceleration in one dimension boils down to these equations:

$$x(t) = x(0) + v(0)t + at^2/2$$ $$v(t) = v(0) + at$$

Here, $x(t)$ is the displacement as a function of time $t$, $v(t)$ is the velocity as a function of time, and $a$ is the constant acceleration. Additionally, $x(0), v(0)$ can be interpreted as your initial displacement and initial velocity.

(To get these two equations, one would start with $dv/dt = a$ and integrate twice with respect to $t$.)

Solve the second equation for $t$, and substitute in the first to eliminate $t$.

Can you take it from here?

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