The height, h, in meters of a dropped object after t seconds can be represented by h (t) = - 4.9 t 2 + 136. What is the instantaneous velocity of the object one second after it is dropped?

Question

Dale Stout

Physics

1 February, 19:16

The height, h, in meters of a dropped object after t seconds can be represented by h (t) = - 4.9 t 2 + 136. What is the instantaneous velocity of the object one second after it is dropped?

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Answers (1)

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Nancy Long · Answer 1

The velocity of the object 1 s after it is dropped is - 9.8 m/s.

Explanation:

Hi there!

The instantaneous velocity is defined by the change in height over a very small time. Mathematically, it is expressed as the derivative of the function h (t):

instantaneous velocity = dh/dt

dh/dt = h' (t) = - 2 · 4.9 · t

h' (t) = - 9.8 · t

Now we have to eveluate the function h' (t) at t = 1 s:

h' (1) = - 9.8 · (1) = - 9.8

The velocity of the object 1 s after it is dropped is - 9.8 m/s.