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A particle is moving in a straight line such that its velocity is increasing at $$5 \text{ m s}^{-1}$$ per meter. The acceleration of the particle is ______ $$\text{m s}^{-2}$$ at a point where its velocity is $$20 \text{ m s}^{-1}$$.
Correct Answer: 100
The velocity is increasing at $$5 \text{ m s}^{-1}$$ per meter. This means:
$$\dfrac{dv}{dx} = 5 \text{ s}^{-1}$$
Acceleration is given by:
$$a = \dfrac{dv}{dt} = \dfrac{dv}{dx} \cdot \dfrac{dx}{dt} = v \cdot \dfrac{dv}{dx}$$
At the point where $$v = 20 \text{ m s}^{-1}$$:
$$a = 20 \times 5 = 100 \text{ m s}^{-2}$$
Therefore, the answer is $$\boxed{100}$$.
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