3 For tgeqslant 1 A particle moves along a line. the distance of the particle from 0 at time t seconds is x metres, where x=(9)/(2t)+t Find the acceleration of the particle when t=3

Question

Answer 1

To find the acceleration of the particle when

, we need to follow these steps:1. **Find the velocity function** by differentiating the position function \( x(t) \) with respect to

.2. **Find the acceleration function** by differentiating the velocity function with respect to

.3. **Evaluate the acceleration function** at

.Given the position function:

### Step 1: Find the Velocity FunctionThe velocity \( v(t) \) is the first derivative of the position \( x(t) \) with respect to

:

Differentiate \( x(t) \):

Using the power rule and the constant multiple rule:

So,

### Step 2: Find the Acceleration FunctionThe acceleration \( a(t) \) is the first derivative of the velocity \( v(t) \) with respect to

:

Differentiate \( v(t) \):

Using the power rule:

So,

### Step 3: Evaluate the Acceleration Function at

Substitute

into the acceleration function:

Therefore, the acceleration of the particle when

is:

Soru