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 can follow these steps:

### Step 1: Understand the given data
We have a table showing the distance covered by a body in successive seconds:
- At 1 second: 2 cm
- At 2 seconds: 6 cm
- At 3 seconds: 10 cm
- At 4 seconds: 14 cm

The body is accelerated uniformly from rest, meaning the initial velocity (u) is 0.

### Step 2: Calculate the acceleration
We can use the distance covered in the first second to find the acceleration (a). The formula for distance covered under uniform acceleration from rest is:

\[ S = ut + \frac{1}{2} a t^2 \]

For the first second (t = 1 s):
- S = 2 cm
- u = 0

Substituting the values into the equation:

\[ 2 = 0 + \frac{1}{2} a (1^2) \]
\[ 2 = \frac{1}{2} a \]
\[ a = 4 \, \text{cm/s}^2 \]

### Step 3: Use the acceleration to find the speed after 4 seconds
Now that we have the acceleration, we can use the formula for final velocity (v):

\[ v = u + at \]

Where:
- u = 0 (initial velocity)
- a = 4 cm/s² (acceleration)
- t = 4 s (time)

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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