A body covers 200 cm in the first 2 sec and 220 cm in the next 4 sec under constant acceleration. Then the velocity of the body after 7 sec is

Options

A. `-15` cm/s
B. 115 cm/s
C. 10 cm/s
D. 20 cm/s

Answer

To solve the problem, we need to determine the velocity of the body after 7 seconds, given that it covers 200 cm in the first 2 seconds and 220 cm in the next 4 seconds under constant acceleration.

### Step-by-Step Solution:

1. **Calculate the distance covered in the first 2 seconds:**
- The body covers a distance \( s_1 = 200 \, \text{cm} \) in the first \( t_1 = 2 \, \text{s} \).

2. **Calculate the distance covered in the next 4 seconds:**
- The body covers a distance \( s_2 = 220 \, \text{cm} \) in the next \( t_2 = 4 \, \text{s} \).

3. **Determine the total distance covered in 6 seconds:**
- The total distance \( s \) covered in the first 6 seconds is:
\[ s = s_1 + s_2 = 200 \, \text{cm} + 220 \, \text{cm} = 420 \, \text{cm} \]

4. **Use the equations of motion:**
- We can use the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
- For the first 2 seconds:
\[ 200 = u(2) + \frac{1}{2} a (2^2) \]
Simplifying gives:
\[ 200 = 2u + 2a \quad \text{(1)} \]

- For the first 6 seconds:
\[ 420 = u(6) + \frac{1}{2} a (6^2) \]
Simplifying gives:
\[ 420 = 6u + 18a \quad \text{(2)} \]

5. **Solve the equations simultaneously:**
- From equation (1):
\[ 2u + 2a = 200 \implies u + a = 100 \quad \text{(3)} \]
- From equation (2):
\[ 6u + 18a = 420 \implies u + 3a = 70 \quad \text{(4)} \]

6. **Subtract equation (3) from equation (4):**
\[ (u + 3a) - (u + a) = 70 - 100 \]
This simplifies to:
\[ 2a = -30 \implies a = -15 \, \text{cm/s}^2 \]

7. **Substitute \( a \) back into equation (3) to find \( u \):**
\[ u + (-15) = 100 \implies u = 115 \, \text{cm/s} \]

8. **Calculate the velocity after 7 seconds:**
- Using the first equation of motion:
\[ v = u + at \]
- For \( t = 7 \, \text{s} \):
\[ v = 115 + (-15)(7) = 115 - 105 = 10 \, \text{cm/s} \]

### Final Answer:
The velocity of the body after 7 seconds is \( 10 \, \text{cm/s} \).