The maximum acceleration of the particle on the interval is 29.45 m/s².
Acceleration: Acceleration is the rate at which velocity changes. Similar to velocity, acceleration is a vector with a magnitude and a direction. For instance, if a car is moving forward straight ahead and accelerating, it is said to be moving forward (positive) and accelerating, and if it is slowing down, it is said to be moving backward (negative).
Acceleration is the change in velocity for each unit change in time.
By taking the first derivative of the equation in this instance, given the velocity equation, we can determine the particle's acceleration.
v'(t) = (t²) (1/t+2) + (t+2) In(t+2).
When t=6 is substituted,
acceleration equals 29.45 m/s².
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Complete question is "A particle moves along the x-axis so that at any time t≥0 its velocity is given by v(t)= t^2In(t+2). What is the acceleration of the particle at time t=6".
