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

Explanation

To solve the problem step by step, we will follow the same reasoning as in the video transcript.

### Step 1: Understanding the Problem
We have a body that travels 200 cm in the first 2 seconds and 220 cm in the next 4 seconds. We need to find the velocity of the body at the end of the 7th second.

### Step 2: Convert Distances to Meters
Since the distances are given in centimeters, we convert them to meters for consistency in SI units.
- Distance in the first 2 seconds: \( s_1 = 200 \, \text{cm} = 2 \, \text{m} \)
- Distance in the next 4 seconds: \( s_2 = 220 \, \text{cm} = 2.2 \, \text{m} \)

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

### Step 4: Apply the Equation of Motion for the Total Distance
Now, we consider the total distance traveled in 6 seconds (200 cm + 220 cm = 420 cm):
\[ s = ut + \frac{1}{2} a t^2 \]
For the total distance in 6 seconds:
\[ 4.2 = u(6) + \frac{1}{2} a (6^2) \]
This simplifies to:
\[ 4.2 = 6u + 18a \quad \text{(2)} \]
Dividing the entire equation by 6:
\[ 0.7 = u + 3a \quad \text{(Equation 2)} \]

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

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

### Step 6: Substitute to Find Initial Velocity
Substituting \( a \) back into Equation 1:
\[ u + (-0.15) = 1 \]
This gives:
\[ u = 1 + 0.15 = 1.15 \, \text{m/s} \]

### Step 7: Find the Velocity at the End of the 7th Second
Using the equation \( v = u + at \):
\[ v = 1.15 + (-0.15)(7) \]
Calculating this gives:
\[ v = 1.15 - 1.05 = 0.10 \, \text{m/s} \]

### Step 8: Convert to Centimeters per Second
To convert the final velocity to centimeters per second:
\[ v = 0.10 \, \text{m/s} = 10 \, \text{cm/s} \]

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

---