Displacement is given by x=2+3t+4t². Find the value of instantaneous acceleration.

To find the value of instantaneous acceleration, we need to take the second derivative of the displacement equation, which represents the rate of change of velocity. Here are the steps to do so:

Step 1: Compute the first derivative of the displacement equation (x) with respect to time (t) to find the velocity equation (v).
x = 2 + 3t + 4t²
v = dx/dt = d/dt(2 + 3t + 4t²)

To differentiate the terms, we use the power rule, which states that if we have a term of the form axⁿ, the derivative is given by anxⁿ⁻¹.

v = 0 + 3 + 8t

Step 2: Differentiate the velocity equation (v) with respect to time (t) to find the acceleration equation (a).
a = dv/dt = d/dt(3 + 8t)

Again, using the power rule to differentiate the terms:

a = 0 + 8

Step 3: Simplify the equation to find the constant value of the instantaneous acceleration.
a = 8

Therefore, the value of the instantaneous acceleration, given the displacement equation x = 2 + 3t + 4t², is 8.

Didn't I just do this?