Determine the instantaneous velocityat t = 8.5 s.

How to find instantaneous speed at a specific time

GIVE ME SOME QUESTION ON INSTANTANEOUS VELOCITY

NUMERICALS OF INSTANTANEOUS VELOCITY

𝑎(𝑡)=8.7𝑡2+6,where 𝑡 is measured in seconds.1. Write an equation for the velocity 𝑣 at time 𝑡. Simplify your answer.𝑣(𝑡)=

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: \[ \boxed{B} \]