Question

Q. What is the acceleration of this object? What is its initial velocity?

For acceleration, can we do the second derivative? I don't know how to do initial velocity.

Answer 1

(1) - v(t) = 9.18t - 1.12

(2) - a(t) = 9.18 m/s²

Step-by-step explanation:

We are given the position function, y(t) = 4.59t² - 1.12t + 0.03. We are asked to determine the following:

1. The velocity function
2. The acceleration function

`\hrulefill`

To find the velocity function simply take the derivative of the position function.

y'(t) = v(t) = 9.18t - 1.12

Using the graph we can find the object's initial velocity by pugging in t=0.220 s.

=> v(0.220) = 9.18(0.220) - 1.12

=> v(0.220) = 0.8996 m/s
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To find the acceleration function either take two derivatives of the position function or one of the velocity function.

y''(t) = v'(t) = a(t) = 9.18 m/s²

Thus, the object is speeding up with constant acceleration.