The distance travelled by an object in time t is given by `s=(2*5)t^2`. The instantaneous speed of the object at `t=5 s` will be :

Options

A. `62.5 ms^(-1)`
B. `12.5 ms^(-1)`
C. `5 ms^(-1)`
D. `25 ms^(-1)`

Answer

To find the instantaneous speed of the object at \( t = 5 \) seconds, we will follow these steps:

### Step 1: Write down the given equation for distance
The distance traveled by the object is given by:
\[ s = (2 \cdot 5)t^2 \]
This simplifies to:
\[ s = 10t^2 \]

### Step 2: Differentiate the distance function to find velocity
The instantaneous speed (or velocity) is the derivative of the distance function with respect to time. Therefore, we differentiate \( s \) with respect to \( t \):
\[ v = \frac{ds}{dt} = \frac{d}{dt}(10t^2) \]
Using the power rule of differentiation, we get:
\[ v = 10 \cdot 2t = 20t \]

### Step 3: Substitute \( t = 5 \) seconds into the velocity equation
Now, we will calculate the instantaneous speed at \( t = 5 \) seconds:
\[ v = 20 \cdot 5 = 100 \text{ m/s} \]

### Final Answer
The instantaneous speed of the object at \( t = 5 \) seconds is:
\[ \boxed{100 \text{ m/s}} \]

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