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Question

For each value below, enter the number correct to two decimal places.

Suppose an arrow is shot upward on a certain planet with a velocity of 25 m/s, then its height in meters after  seconds is given by .

A) Find the instantaneous velocity at seconds.

B) Find the acceleration at seconds.

Answer 1

A) velocity v(t) = 25 - 23.2t m/s; v(0.8) = 25 - 23.2·0.8 = 6.44 m/s.

B) acceleration a(t) = - 23.2 m/s²; a(0.8) = - 23.8 m/s².

Answer 2

Use the following property:

Let the height, vertical velocity, and vertical acceleration at time t be h(t), v(t), and a(t) respectively. Then

v(t) = h'(t) (i.e., the derivative of h(t) with respect to t), and

a(t) = v'(t) = a''(t) (i.e., the derivative of v(t) with respect to t.

So, in particular, if h(t) = A t + B t^2, where A and B are constants, then

v(t) = A + 2 B t, and

a(t) = 2 B.

In your question, A = 25, and B = - 11.6. You should do the rest.