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The distance travelled by an object in time $$t$$ is given by $$s = 2.5t^2$$. The instantaneous speed of the object at $$t = 5$$ s will be :
Given: $$s = 2.5t^2$$
Instantaneous speed is the derivative of distance with respect to time:
$$v = \frac{ds}{dt} = 2 \times 2.5t = 5t$$
At $$t = 5$$ s:
$$v = 5 \times 5 = 25 \text{ m/s}$$
The instantaneous speed is $$\mathbf{25}$$ m/s.
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