Finding deceleration and initial speed, given time and distance

Question

(I'm sorry if this is a bad way to frame a math question)

Let's say a car is moving at 40m/s and a brake is applied, the car decelerates at 10m/s thus stops after 4 seconds, traveled 100m after the brake is applied.

Now a different car is moving at unknown speed, a brake with different deceleration is applied and the car stops after 8 seconds, but also traveled 100m.

Is it possible to find out what is the initial speed AND the deceleration of the second car?

Example Picture

I have been trying to find if there's a formula to this, but i can only find either the formula include time or distance, but not both.

Answer 1

You can use the usual $s=x_0+v_0t+\frac 12at^2, v=v_0+at$ formulas. We are given $x_0=0$ because we measure from there. We are given $v(8)=0$, so $a=-\frac {v_0}8$. We are also told $s(8)=100$ You have two equations in two unknowns, $a, v_0$.

Added: plugging in to $s(8)=100$ we get $100=8v_0+\frac 12 (-\frac {v_0}8)8^2$ or $100=4v_0, v_0=25, a=-\frac {25}8$

Answer 2

I mean you could use the kinematic equations

Vf^2 = Vi^2 + 2A(Xf-Xi) Xf - Xi =Vit + .5At^2 and then rearrange to get Vf^2 = (( Xf - Xi - .5At^2)/t)^2+ 2A(Xf-Xi) We know that Vf = 0 Soo 0 = (( 100 - 32A)/8)^2 + 200A No you can rearrange and solve for A