A particle moves in a straight line such that its displacement, $s$ metres, from a fixed point, at time $t$ seconds, $t \geqslant 0$, is given by $s=(1+3 t)^{-\frac{1}{2}}$. (ii) Show that the acceleration of the particle will never be zero.

Explanation

To show that the acceleration of the particle will never be zero, we first need to find the acceleration function. We differentiate the velocity function v = -3/2 (1 + 3t)^(-3/2) with respect to time t. We get a = d/dt (-3/2 (1 + 3t)^(-3/2)) = (-3/2) * (-3/2) (1 + 3t)^(-5/2) = 9/4 (1 + 3t)^(-5/2). Since the acceleration function is always positive, the acceleration of the particle will never be zero.

A particle moves in a straight line such that its displacement, $s$ metres, from a fixed point, at time $t$ seconds, $t \geqslant 0$, is given by $s=(1+3 t)^{-\frac{1}{2}}$. (ii) Show that the acceleration of the particle will never be zero.

Explanation

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