The table shows the distance covered in successive seconds by a body accelerated uniformly from rest
`{:("Time interval (s)", I, II, III, IV),("Distance (cm)", 2,6,10,14):}`
What is the speed of the body after 4 sec ?

Options

A. 4 cm/sec
B. 8 cm/sec
C. 14 cm/sec
D. 16 cm/sec

Answer

To find the speed of the body after 4 seconds, we will follow these steps:

### Step 1: Understand the given data
We have a table that shows the distance covered by a body in successive seconds:
- 1st second: 2 cm
- 2nd second: 6 cm
- 3rd second: 10 cm
- 4th second: 14 cm

### Step 2: Calculate the total distance covered in each second
To find the distance covered in each second, we can calculate the distance for each second as follows:
- Distance covered in the 1st second = 2 cm
- Distance covered in the 2nd second = 6 cm - 2 cm = 4 cm
- Distance covered in the 3rd second = 10 cm - 6 cm = 4 cm
- Distance covered in the 4th second = 14 cm - 10 cm = 4 cm

### Step 3: Determine the acceleration
Since the body is accelerating uniformly from rest, we can use the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s \) is the distance covered in the first second (which is 2 cm)
- \( u \) is the initial velocity (0 cm/s, since it starts from rest)
- \( a \) is the acceleration
- \( t \) is the time (1 second)

Substituting the values into the equation:
\[ 2 = 0 \cdot 1 + \frac{1}{2} a (1^2) \]
This simplifies to:
\[ 2 = \frac{1}{2} a \]
Multiplying both sides by 2 gives:
\[ a = 4 \, \text{cm/s}^2 \]

### Step 4: Use the acceleration to find the speed after 4 seconds
Now we can use the formula for final velocity:
\[ v = u + at \]
Where:
- \( v \) is the final velocity
- \( u \) is the initial velocity (0 cm/s)
- \( a \) is the acceleration (4 cm/s²)
- \( t \) is the time (4 seconds)

Substituting the values:
\[ v = 0 + (4 \, \text{cm/s}^2)(4 \, \text{s}) \]
\[ v = 16 \, \text{cm/s} \]

### Conclusion
The speed of the body after 4 seconds is **16 cm/s**.

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