Calculating Final Velocity: Dragsters

Problema e solução em inglês, como no livro original.

Calculate the final velocity of the dragster in Example 2.10 without using information about time.

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

Estratégia
Draw a sketch.

Figure 2.33
The equation $v^{2} = v_{0}^{2} + 2 a (x - x_{0})$ is ideally suited to this task because it relates velocities, acceleration, and displacement, and no time information is required.
Solução
1. Identify the known values. We know that $v_{0} = 0$ , since the dragster starts from rest. Then we note that $x - x_{0} = 402 m$ (this was the answer in Example 2.10). Finally, the average acceleration was given to be $a = 26 . {0 m/s}^{2}$ .
2. Plug the knowns into the equation $v^{2} = v_{0}^{2} + 2 a (x - x_{0})$ and solve for $v .$
$v^{2} = 0 + 2 (26 . {0 m/s}^{2}) (402 m) .$
2.47

Thus

$v^{2} = 2 . 09 \times 10^{4} m^{2} {/s}^{2} .$
2.48

To get $v$ , we take the square root:

$v = \sqrt{2 . 09 \times 10^{4} m^{2} {/s}^{2}} = 145 m/s .$
2.49
Discussão
145 m/s is about 522 km/h or about 324 mi/h, but even this breakneck speed is short of the record for the quarter mile. Also, note that a square root has two values; we took the positive value to indicate a velocity in the same direction as the acceleration.

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