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2 years ago

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Joseph DeLoach of the United States set an Olympic record in 1988 for the 200-meter dash with a time of 19.75 seconds. What was

his average speed? Give your answer in meters per second and miles per hour.

1 answer:

Lera25 [3.4K]2 years ago

7 0

Answer:

The average speed was 10.12 m/s or 22.96 mi/h

Explanation:

The average speed is defined as:

$v = \frac{d}{t}$ (1)

Where d is the total distance traveled and t is the passed time.

For the special case of Joseph DeLoach, he traveled a total distance of 200 meters in 19.75 seconds. Those values can be introduced in equation 1:

$v = \frac{200 m}{19.75 s}$

$v = 10.12 m/s$

That means that Joseph DeLoach traveled a distance of 10.12 meters per second.

To represent the result in miles per hour, it is necessary to know that 1 mile is equivalent to 1609 meters.

$200 m x \frac{1 mi}{1609 m}$ ⇒ 0.124 mi

it is needed to express the given time in units of hour. 1 hour is equivalent to 3600 seconds.

$19.75 s x \frac{1 h}{3600 s}$ ⇒ 0.0054 h

Then, equation 1 is used with the new representation of the values.

$v = \frac{0.124 mi}{0.0054 h}$

$v = 22.96 mi/h$

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Answer:

Part a)

$\omega = 8.17 rad/s$

Part b)

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Part c)

$\alpha = 0.69 rad/s^2$

Part d)

$\alpha = 0.48 rad/s^2$

Part e)

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Explanation:

Part a)

Angular speed is given as

$\omega = 2\pi f$

$\omega = 2\pi(\frac{78}{60})$

$\omega = 8.17 rad/s$

Part b)

Since turn table is accelerating uniformly

so we will have

$\theta = \frac{\omega_f + \omega_i}{2} t$

$\theta = \frac{8.17 + 0}{2}(11.9)$

$2N\pi = 48.6$

$N = 7.74 rev$

Part c)

angular acceleration is given as

$\alpha = \frac{\omega_f - \omega_i}{t}$

$\alpha = \frac{8.17 - 0}{11.9}$

$\alpha = 0.69 rad/s^2$

Part d)

When its angular speed changes to 120 rpm

then we will have

$\omega_2 = 2\pi (\frac{120}{60})$

$\omega_2 = 12.56 rad/s$

number of turns revolved is 15 times

so we have

$\omega_f^2 - \omega_i^2 = 2 \alpha \theta$

$12.56^2 - 8.17^2 = 2\alpha (2\pi\times 15)$

$\alpha = 0.48 rad/s^2$

Part e)

now for uniform acceleration we have

$\omega_f - \omega_i = \alpha t$

$12.56 - 8.17 = 0.48 t$

$t = 9.14 s$

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Answer:

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