A particle of mass 10 kg is moving in a straight line. If its displacement, x with time tis given by `x=(t^(3)-2t-10)m` then the force acting on it at the end of 4 seconds is

Options

A. 24N
B. 240N
C. 300N
D. 1200N

Explanation

To solve the problem step by step, we need to find the force acting on a particle of mass 10 kg, given its displacement as a function of time. The displacement is given by the equation:

\[ x(t) = t^3 - 2t - 10 \, \text{m} \]

### Step 1: Find the velocity of the particle
The velocity \( v \) is the first derivative of displacement \( x \) with respect to time \( t \).

\[ v(t) = \frac{dx}{dt} = \frac{d}{dt}(t^3 - 2t - 10) \]

Calculating the derivative:

\[ v(t) = 3t^2 - 2 \]

### Step 2: Find the acceleration of the particle
The acceleration \( a \) is the derivative of velocity \( v \) with respect to time \( t \).

\[ a(t) = \frac{dv}{dt} = \frac{d}{dt}(3t^2 - 2) \]

Calculating the derivative:

\[ a(t) = 6t \]

### Step 3: Calculate the acceleration at \( t = 4 \) seconds
Now, we substitute \( t = 4 \) seconds into the acceleration equation:

\[ a(4) = 6 \times 4 = 24 \, \text{m/s}^2 \]

### Step 4: Calculate the force acting on the particle
Using Newton's second law, the force \( F \) is given by:

\[ F = m \cdot a \]

Where \( m = 10 \, \text{kg} \) and \( a = 24 \, \text{m/s}^2 \):

\[ F = 10 \, \text{kg} \times 24 \, \text{m/s}^2 = 240 \, \text{N} \]

### Final Answer
The force acting on the particle at the end of 4 seconds is:

\[ \boxed{240 \, \text{N}} \]

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