The displacement s of an object is given as a function of time t
`s=5t^(2)+9t`
Calculate the instantaneous velocity of object at t = 0.

Explanation

To find the instantaneous velocity of the object at \( t = 0 \), we need to follow these steps:

### Step 1: Understand the given function
The displacement \( s \) of the object is given by the equation:
\[ s = 5t^2 + 9t \]
This equation describes how the position of the object changes with time.

### Step 2: Differentiate the displacement function
To find the instantaneous velocity, we need to differentiate the displacement function \( s \) with respect to time \( t \). The instantaneous velocity \( v \) is given by:
\[ v = \frac{ds}{dt} \]
Now, we differentiate \( s \):
\[ \frac{ds}{dt} = \frac{d}{dt}(5t^2 + 9t) \]

### Step 3: Apply the power rule of differentiation
Using the power rule, we differentiate each term:
- The derivative of \( 5t^2 \) is \( 10t \) (using \( \frac{d}{dt}(t^n) = nt^{n-1} \)).
- The derivative of \( 9t \) is \( 9 \).

Putting it all together, we have:
\[ \frac{ds}{dt} = 10t + 9 \]

### Step 4: Substitute \( t = 0 \)
Now, we need to find the instantaneous velocity at \( t = 0 \):
\[ v(0) = 10(0) + 9 \]
Calculating this gives:
\[ v(0) = 0 + 9 = 9 \text{ m/s} \]

### Conclusion
The instantaneous velocity of the object at \( t = 0 \) is:
\[ \boxed{9 \text{ m/s}} \]

---