# A particle moves along a straight line such that its displacement any time t is given by: s=( #t^3 - 3t^2 +2#)m. The displacement when the acceleration becomes zero is?

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#t^3 - 3t^2 +2#

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The displacement when the acceleration becomes zero can be found by first finding the expression for acceleration (a), which is the second derivative of displacement (s) with respect to time (t), and then determining the value of time (t) when acceleration (a) equals zero. Finally, substituting this value of time (t) into the displacement equation (s) will give the displacement at that point.

Given displacement equation: s = t^3 - 3t^2 + 2

The acceleration (a) can be found by taking the second derivative of displacement equation (s) with respect to time (t): a = d^2s/dt^2

Now, differentiate the displacement equation twice: s = t^3 - 3t^2 + 2 v = ds/dt = 3t^2 - 6t a = dv/dt = d^2s/dt^2 = 6t - 6

To find when acceleration (a) equals zero, set the expression for acceleration equal to zero and solve for time (t): 6t - 6 = 0 6t = 6 t = 1

Now that we have the time (t) when acceleration (a) becomes zero, substitute this value into the displacement equation (s) to find the displacement at that point: s = t^3 - 3t^2 + 2 s = (1)^3 - 3(1)^2 + 2 s = 1 - 3 + 2 s = 0

Therefore, the displacement when the acceleration becomes zero is 0 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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