Find the velocity at t = 0.69 using the following equation defining position.

p(t) = 2t3 - 4t2 +11t -2

Round to 2 decimal places.

Question

Find the velocity at t = 0.69 using the following equation defining position.

p(t) = 2t3 - 4t2 +11t -2

Round to 2 decimal places.

BlackTom AI · Accepted Answer

We are asked to find the velocity at t = 0.69 given p(t) = 2t^3 - 4t^2 + 11t - 2. 
First, recall that velocity is the derivative of position: v(t) = p'(t).
Compute the derivative term by term: d/dt[2t^3] = 6t^2, d/dt[-4t^2] = -8t, d/dt[11t] = 11, and d/dt[-2] = 0. 
Thus, v(t) = 6t^2 - 8t + 11.
Next, substitute t = 0.69 into the velocity function: t^2 = 0.69^2 = 0.4761. So 6t^2 = 6 × 0.4761 = 2.8566. Then -8t = -8 × 0.69 = -5.52. Add 11 to complete the expression: v(0.69) = 2.8566 - 5.52 + 11.
Compute the sum: 2.8566 - 5.52 = -2.6634; adding 11 gives 8.3366. 
Round to two decimal places as requested: 8.34. 
Therefore, v(0.69) ≈ 8.34. 
If you want to check the arithmetic, you can keep more decimal places during the intermediate steps and only round at the end to two decimals.

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Find the velocity at t = 0.69 using the following equation defining position. p(t) = 2t3 - 4t2 +11t -2 Round to 2 decimal places.

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