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A particle moves along a straight line such that its position x at time t is given by x = 1/(1 + t^5). Find the velocity and acceleration of the particle at t = 1.

1. distance x = 1/(1 + 5)
2. velocity v = dx/dt = -1/((1 + 5)^2)
3. acceleration a = d^2x/dt^2 = 2x^3
4. None of these

Correct answer: None of these

Solution

To solve, we first find the velocity v = dx/dt and acceleration a = d²x/dt². The given options for velocity and acceleration are incorrect upon differentiation. Thus, the correct answer is 'None of these.'

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