A body falls for 5 s from rest. If the acceleration due to gravity of earth ceases to act, the distance it travels in the next 3 s is

Options

A. 73.5 m
B. 294 m
C. 147 m
D. 49 m

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the Problem
We have a body that falls freely under the influence of gravity for 5 seconds. After this time, the acceleration due to gravity ceases to act, and we need to find the distance it travels in the next 3 seconds.

### Step 2: Calculate the Final Velocity After 5 Seconds
Since the body is falling freely from rest, we can use the kinematic equation to find the final velocity after 5 seconds.

The formula is:
\[ v = u + at \]
Where:
- \( u \) = initial velocity = 0 (since it starts from rest)
- \( a \) = acceleration due to gravity = \( 9.8 \, \text{m/s}^2 \)
- \( t \) = time = 5 seconds

Substituting the values:
\[ v = 0 + (9.8 \, \text{m/s}^2)(5 \, \text{s}) \]
\[ v = 49 \, \text{m/s} \]

### Step 3: Analyze Motion After Gravity Ceases
After 5 seconds, the body has a velocity of \( 49 \, \text{m/s} \) and there is no further acceleration acting on it (gravity ceases to act). Therefore, the body will continue to move with this constant velocity.

### Step 4: Calculate the Distance Traveled in the Next 3 Seconds
Since there is no acceleration, we can use the formula for distance traveled at constant velocity:
\[ s = ut + vt \]
Where:
- \( u \) = initial velocity = \( 49 \, \text{m/s} \)
- \( t \) = time = 3 seconds

Substituting the values:
\[ s = (49 \, \text{m/s})(3 \, \text{s}) \]
\[ s = 147 \, \text{m} \]

### Final Answer
The distance traveled by the body in the next 3 seconds is **147 meters**.

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