The displacement x of an object is given as a function of time, x = 2t + 3t². This means that the displacement of the object changes as time passes according to this function. At any given time t, we can calculate the displacement x of the object using this function.


To calculate the instantaneous velocity of the object at t = 2, we need to find the derivative of the displacement function with respect to time:

x = 2t + 3t²
dx/dt = 2 + 6t

Now, we can substitute t = 2 into this equation to find the instantaneous velocity at t = 2:

dx/dt = 2 + 6t
dx/dt = 2 + 6(2)
dx/dt = 14

Therefore, the instantaneous velocity of the object at t = 2 is 14 units per second.


The positive value of the instantaneous velocity indicates that the object is moving in the positive direction. The units of the velocity are determined by the units of the displacement function (in this case, units of distance per unit of time).

It is important to note that the instantaneous velocity only gives us information about the object's velocity at a single moment in time. To fully understand the object's motion, we would need to analyze its velocity over a range of time intervals.

X=2t+3t^2
dx/dt =v=2+6t
2+6×2=14m/s