Given the following acceleration function of an object moving along a line, find the position function with the given initial ve

Question

2 years ago

11

locity and position
a(t) = -40, (O) = 18, S(O) = 0

1 answer:

nalin [4] · Answer 1 · 2023-07-30T19:11:36+03:00

The position function for the given object is:

s(t) = (-20 m/s^2)*t^2 + (18m/s)*t

<h3>How to get the position function?</h3>

Here we know that:

a(t) = -40 m/s^2

v(0) = 18 m/s

s(0) = 0m

So, we know the acceleration, the initial velocity, and the initial position.

To get the velocity equation we need to integrate the acceleration equation, we will get:

v(t) = (-40 m/s^2)*t + C

Where C is the constant of integration, which we know that is the initial velocity, then:

v(t) = (-40 m/s^2)*t + 18m/s

Now, to get the position equation, we need to integrate again:

s(t) = (1/2)*(-40 m/s^2)*t^2 + (18m/s)*t + s(0)

s(t) = (-20 m/s^2)*t^2 + (18m/s)*t

So, the position function, is: s(t) = (-20 m/s^2)*t^2 + (18m/s)*t

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