ow would we calculate the speed of the object at t = 3 seconds?

What is the equation to calculate speed?

An object starts from rest and falls freely. What is the speed of the object at the end of 3.00 seconds?A 9.81 m/sB 19.6 m/sC 29.4 m/sD 88.2 m/s

Object A moved 40 m in 1 minute while Object B moved 40 km in 1 minute.Which object was faster?

How to find instantaneous speed at a specific time

To find the velocity of the object in terms of time, we need to take the derivative of the displacement function \(s(t)\) with respect to time \(t\). The displacement function is given by: \[ s(t) = 8t^3 - 3t^2 - 4 \] The velocity \(v(t)\) is the first derivative of the displacement \(s(t)\) with respect to time \(t\): \[ v(t) = \frac{ds(t)}{dt} \] Let's differentiate \(s(t)\): \[ s(t) = 8t^3 - 3t^2 - 4 \] Using the power rule for differentiation, which states that \(\frac{d}{dt}[t^n] = nt^{n-1}\), we get: \[ \frac{d}{dt}[8t^3] = 8 \cdot 3t^{3-1} = 24t^2 \] \[ \frac{d}{dt}[-3t^2] = -3 \cdot 2t^{2-1} = -6t \] \[ \frac{d}{dt}[-4] = 0 \] Combining these results, we get: \[ v(t) = 24t^2 - 6t \] Therefore, the correct answer is: \[ \boxed{B} \]