Five persons A, B, C, D and E are pulling a cart of mass 100 kg on a smooth surface and the cart is moving with an acceleration of `3ms^(-2)` in the east direction. If another person F comes and ans starts pulling the cart with a force of 100 N due west , then the acceleration of the cart will be

Options

A. `2.5 ms^(-2)`
B. `1 ms^(-2)`
C. `2 ms^(-2)`
D. `4 ms^(-2)`

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Calculate the initial force exerted by persons A, B, C, D, and E.
The cart has a mass of 100 kg and is accelerating at 3 m/s². According to Newton's second law, the net force (F') acting on the cart can be calculated using the formula:

\[ F' = m \cdot a \]

Where:
- \( m \) is the mass of the cart (100 kg)
- \( a \) is the acceleration (3 m/s²)

Substituting the values:

\[ F' = 100 \, \text{kg} \cdot 3 \, \text{m/s}^2 = 300 \, \text{N} \]

### Step 2: Determine the net force after person F pulls the cart.
Person F pulls the cart with a force of 100 N due west. Since the initial force (F') is directed east, we need to consider the direction of the forces. The net force (F_net) can be calculated as:

\[ F_{\text{net}} = F' - F \]

Where:
- \( F' = 300 \, \text{N} \) (east)
- \( F = 100 \, \text{N} \) (west)

Substituting the values:

\[ F_{\text{net}} = 300 \, \text{N} - 100 \, \text{N} = 200 \, \text{N} \]

### Step 3: Calculate the new acceleration of the cart.
Now that we have the net force, we can calculate the new acceleration (a') of the cart using Newton's second law again:

\[ F_{\text{net}} = m \cdot a' \]

Rearranging the formula to find acceleration:

\[ a' = \frac{F_{\text{net}}}{m} \]

Substituting the values:

\[ a' = \frac{200 \, \text{N}}{100 \, \text{kg}} = 2 \, \text{m/s}^2 \]

### Final Answer:
The new acceleration of the cart is \( 2 \, \text{m/s}^2 \) in the east direction.

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