A body travels 200 cm in the first two seconds and 220 cm in the next 4 seconds with deceleration the velocity of the body at the end of the `7^(th)` second is

Options

A. 20 cm/s
B. 15 cm/s
C. 10 cm/s
D. 0 cm/s

Explanation

To solve the problem step by step, we need to analyze the motion of the body using the equations of motion.

### Step 1: Understand the given data
- The body travels 200 cm in the first 2 seconds.
- The body travels 220 cm in the next 4 seconds (from 2 seconds to 6 seconds).

### Step 2: Convert distances to meters
- 200 cm = 2 m
- 220 cm = 2.2 m

### Step 3: Use the first equation of motion for the first 2 seconds
Using the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
For the first 2 seconds (t = 2 s):
\[ 2 = u(2) + \frac{1}{2} a (2^2) \]
This simplifies to:
\[ 2 = 2u + 2a \]
Dividing the entire equation by 2:
\[ 1 = u + a \] (Equation 1)

### Step 4: Use the second equation of motion for the first 6 seconds
Now, we consider the total distance traveled in the first 6 seconds:
The total distance is:
\[ 200 \text{ cm} + 220 \text{ cm} = 420 \text{ cm} = 4.2 \text{ m} \]
Using the same equation of motion for 6 seconds (t = 6 s):
\[ 4.2 = u(6) + \frac{1}{2} a (6^2) \]
This simplifies to:
\[ 4.2 = 6u + 18a \]
Dividing the entire equation by 6:
\[ 0.7 = u + 3a \] (Equation 2)

### Step 5: Solve the equations simultaneously
Now we have two equations:
1. \( 1 = u + a \)
2. \( 0.7 = u + 3a \)

Subtract Equation 1 from Equation 2:
\[ (0.7 - 1) = (u + 3a) - (u + a) \]
This simplifies to:
\[ -0.3 = 2a \]
Thus:
\[ a = -0.15 \text{ m/s}^2 \] (deceleration)

### Step 6: Substitute the value of 'a' back to find 'u'
Using Equation 1:
\[ 1 = u + (-0.15) \]
Thus:
\[ u = 1 + 0.15 = 1.15 \text{ m/s} \]

### Step 7: Find the velocity at the end of 7 seconds
Using the equation of motion:
\[ v = u + at \]
Where:
- \( u = 1.15 \text{ m/s} \)
- \( a = -0.15 \text{ m/s}^2 \)
- \( t = 7 \text{ s} \)

Substituting the values:
\[ v = 1.15 + (-0.15)(7) \]
\[ v = 1.15 - 1.05 \]
\[ v = 0.1 \text{ m/s} \]

### Step 8: Convert the velocity to cm/s
\[ v = 0.1 \text{ m/s} = 10 \text{ cm/s} \]

### Final Answer
The velocity of the body at the end of the 7th second is **10 cm/s**.

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