An astronaut is accelerated in his spacecraft from rest to 800 mi./hr. In 60 sec. He was subjected to an acceleration of

Options

A. 4800 ft./sec./sec.
B. 1200 mi. /`hr^2`
C. 4800 mi./`hr^2`
D. 48000mi./`hr^2`

Explanation

To solve the problem, we need to calculate the acceleration experienced by the astronaut in the spacecraft. Let's break it down step by step.

### Step 1: Identify the given values
- Initial velocity (u) = 0 miles per hour (since the astronaut starts from rest)
- Final velocity (v) = 800 miles per hour
- Time (t) = 60 seconds

### Step 2: Convert time from seconds to hours
Since the final velocity is given in miles per hour, we need to convert the time from seconds to hours for consistency.
- \( t = 60 \text{ seconds} = \frac{60}{3600} \text{ hours} = \frac{1}{60} \text{ hours} \)

### Step 3: Use the first equation of motion
The first equation of motion relates initial velocity, final velocity, acceleration, and time:
\[ v = u + at \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step 4: Substitute the known values into the equation
Since \( u = 0 \):
\[ 800 = 0 + a \left(\frac{1}{60}\right) \]
This simplifies to:
\[ 800 = a \left(\frac{1}{60}\right) \]

### Step 5: Solve for acceleration (a)
To find \( a \), multiply both sides by 60:
\[ a = 800 \times 60 \]
\[ a = 48000 \text{ miles per hour}^2 \]

### Final Answer
The astronaut was subjected to an acceleration of **48000 miles per hour²**.

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