Question

An object's velocity is given by v(t) = 2t + 3/t^2. What is the object's velocity when its acceleration is zero?

A) v = 0
B) v = 1
C) v = -1
D) v = 2

Answer 1

The object's velocity when its acceleration is zero is v = 2 + 2((3/2)^(1/3)).

Step-by-step explanation:

To find the object's velocity when its acceleration is zero, we need to find the time at which the acceleration is zero and then substitute that value of time into the velocity function. The acceleration can be found by taking the derivative of the velocity function. In this case, the acceleration function is a(t) = 2 - 6/t^3. Setting the acceleration equal to zero, we get 2 - 6/t^3 = 0, which gives us t^3 = 3/2 or t = (3/2)^(1/3). Substituting this value of t into the velocity function, we get v((3/2)^(1/3)) = 2((3/2)^(1/3)) + 3/((3/2)^(1/3))^2 = 2((3/2)^(1/3)) + 3(2/3)^2 = 2((3/2)^(1/3)) + 2 = 2 + 2((3/2)^(1/3)). So, the object's velocity when its acceleration is zero is v = 2 + 2((3/2)^(1/3)).