The motion of a particle along a straight line is described by the equation x = 2t^4 -3t^3. Determine the acceleration after 3s

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Explanation:

In this problem, we know that the position of the particle is described by the equation

where t is the time.

The velocity of the particle can be calculated as the derivate of the position; so we find:

Similarly, the acceleration of the particle can be found by calculating the derivative of the velocity.

By doing so, we find an expression for the acceleration:

Therefore, this is the expression for the acceleration of the particle.

Now we want to find the acceleration after 3 s. To do so, we substitute the value of t = 3 into the expression above; so we find:

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