The displacement s of an object is given as a function of time t by the following equation `s=2t+5t^(2)+3t^(3)`. Calculate the instantaneous velocity of the object at t = 1 s.

Explanation

To find the instantaneous velocity of the object at \( t = 1 \) second, we will follow these steps:

### Step 1: Write down the displacement function
The displacement \( s \) of the object is given by the equation:
\[ s(t) = 2t + 5t^2 + 3t^3 \]

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

Differentiating \( s(t) \):
\[ \frac{ds}{dt} = \frac{d}{dt}(2t) + \frac{d}{dt}(5t^2) + \frac{d}{dt}(3t^3) \]

Calculating each term:
- The derivative of \( 2t \) is \( 2 \).
- The derivative of \( 5t^2 \) is \( 10t \).
- The derivative of \( 3t^3 \) is \( 9t^2 \).

Thus, we have:
\[ \frac{ds}{dt} = 2 + 10t + 9t^2 \]

### Step 3: Substitute \( t = 1 \) into the velocity function
Now, we will find the instantaneous velocity at \( t = 1 \) second by substituting \( t = 1 \) into the velocity function:
\[ v(1) = 2 + 10(1) + 9(1)^2 \]

Calculating this:
\[ v(1) = 2 + 10 + 9 = 21 \, \text{m/s} \]

### Conclusion
The instantaneous velocity of the object at \( t = 1 \) second is:
\[ \boxed{21 \, \text{m/s}} \]

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