Car overtaking

A passenger car travels at a speed of 30 m/s; before it travels, a freight truck drives at a constant speed of 10 m/s. Within 30 meters of the truck, the driver of the car finds out that the truck can not overtake. That's why it starts braking with an acceleration of 5 m/s. Will cars collide? If so, how big were the car's speeds at the collision?

Correct answer:

v₂₂ =  12.6795 m/s

Step-by-step explanation:

$$\begin{gathered} v_1=10\text{m/s} \\ {v}_2=30\text{m/s} \\ s=30\text{m} \\ a=5{\text{m/s}}^2 \\ v=v_2-v_1=30-10=20\text{m/s} \\ s=\frac{1}{2}a{t}^2 \\ t=\sqrt{2\cdot s/a}=\sqrt{2\cdot 30/5}=2\sqrt{3}\text{s}\doteq 3.4641\text{s} \\ {v}_{22}=v_2-a\cdot t=30-5\cdot 3.4641\doteq 12.6795\text{m/s} \\ {v}_{22}>v_1 \end{gathered}$$

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