Chapter 12: Q27P (page 535)

A cop pulls you over and asks what speed you were going. “Well, officer, I cannot tell a lie: the speedometer read $4 \times 10^{8} m / s$ .” He gives you a ticket, because the speed limit on this highway is $2.5 \times 10^{8} m / s$ . In court, your lawyer (who, luckily, has studied physics) points out that a car’s speedometer measures proper velocity, whereas the speed limit is ordinary velocity. Guilty, or innocent?

Short Answer

Expert verified

The driver is innocent.

Step by step solution

Expression for the relationship between proper velocity and ordinary velocity:

Write the relationship between proper and ordinary velocity.

$u = \frac{1}{{\sqrt{1 - \frac{η^{2}}{c^{2}}}}^{η}}$ …… (1)

Here, $η$ is the proper velocity, u is the ordinary velocity, and c is the speed of light.

Determine that the driver is guilty or innocent:

Substitute $4 \times 10^{8} m / s$ for $η$ and $3 \times 10^{8} m / s$ for $c$ in equation (1).

$u - \frac{1}{\sqrt{1 - \frac{{(4 \times 10^{8} m / s)}^{2}}{{(3 \times 10^{8} m / s)}^{2}}}} (4 \times 10^{8} m / s) u - (0.6) \times (4 \times 10^{2} m / s) u - 2.4 \times 10^{8} m / s$

As the ordinary velocity is less than the speed light $(u < s)$ , the driver maintained his car’s speed, and hence lawyer proved him innocent.

Therefore, the driver is innocent.

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Short Answer

Step by step solution

Expression for the relationship between proper velocity and ordinary velocity:

Determine that the driver is guilty or innocent:

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