The position equation for a particle is s of t equals the square root of the quantity t cubed plus 1 where s is measured in feet and t is measured in seconds. find the acceleration of the particle at 2 seconds.

1 ft/sec2
two thirds ft/sec2
negative 1 over 108 ft/sec2
none of these

Acceleration of the particle is two thirds ft/s².

Step-by-step explanation:

It is given that, the position of the particle at time t is given by :

Where

s is in feet

t is in seconds

We need to find the acceleration of the particle at 2 seconds. Firstly calculating the velocity of the particle as :

This gives,

Since,

At t = 2 seconds,

or

So, the acceleration of the particle at 2 seconds is 2/3 ft/s². Hence, this is the required solution.

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