MATHEMATICS COLLEGE

Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a=16, v(0) = -14, s(0) = -8

Answers

Answer 1

Answer:

Answer:

The position at time t is $s(t) = 8t^2 - 14t -8$

Step-by-step explanation:

From the question we are told that

The acceleration is $a = 16$

The velocity at t = 0 is $v(0) = -14$

The position at time t = 0 is $s(0) = -8$

Generally acceleration is mathematically represented as

$a(t) = (d v)/(dt )$

=> $(dv)/(dt) = 16$

=> $dv = 16 dt$

integrating both sides we have

$\int\limits dv = \int\limits16 dt$

=> $v(t) = 16 t + c$

Now at t = 0

$v(0) = 16 * 0 +c = -14$

=> $c = -14$

$v(t) = 16 t -14$

Generally the position of the body is mathematically represented as

$s(t) = \int\limits v(t)dt$

$s(t) = \int\limits 16t - 14 dt$

$s(t) = 16 (t^2)/(2) - 14t + C$

Now at t = 0

$s(0) = 16 (0^2)/(2) - 14(0) + C = -8$

=> $C = -8$

$s(t) = 8t^2 - 14t -8$

Answer 2

Answer:

Final answer:

The position of the body at time t, given an acceleration of 16 m/s², an initial velocity of -14 m/s and an initial position of -8 m, is given by the equation s(t) = -8 - 14t + 8t².

Explanation:

In your problem, you're asked to find the body's position at time t given its acceleration, initial velocity, and initial position. We can do this by utilizing basic kinematics, specifically the equation for position under constant acceleration. This equation is: s(t) = s(0) + v(0)t + 0.5at².

Substituting the given values into the formula, we get s(t) = -8 + -14t + 0.5*16t².

This is the equation for the body's position at time t. It can be simplified further by multiplying the terms inside, leading to s(t) = -8 - 14t + 8t².

Therefore, given an acceleration of 16 m/s², an initial velocity of -14 m/s and an initial position of -8 m, the position of the body at time t can be described by the equation s(t) = -8 - 14t + 8t².

Learn more about Kinematics here:

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Answers

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Step-by-step explanation:

From Oxford, getting to Kingswood takes 7.5mi, and getting to Norwood takes 11.8mi. Thus, simply do 11.8-7.5 to get 4.3mi.

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Solve for x:

4x + 8 = 5x + 2

Answers

Answer: X = 6

Step-by-step explanation:

4x + 8 = 5x + 2

-5x -5x (minus 5x from each side)

-x+8=2

-8 from each side

-x = -6

divided by -1 from each side

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4x+8 = 5x +2
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Find the surface area of the cube shown below. units 2 2 squared

Answers

The surface area of the cube with a side length of 2 units is 24 units squared

How to determine the surface area?

The side length of the cube is given as:

l = 2

The surface area is calculated as:

Surface area = 6l^2

This gives

Surface area = 6 *2^2

Evaluate

Surface area = 24

Hence, the surface area of the cube is 24 unit squared

Answers

Answer:Yes

Step-by-step explanation:

In the question it is given that jenny is either a hippie or an artist .so there are two possibilities for jenny .

Further it is given that jenny is certainly not a hippie therefore one possibility is ruled out of being a hippie so we left with only one i.e. jennny being a artist.

So we can conclude that jenny is an artist

Answer:

yes

Step-by-step explanation:

there is only 1 reasonable answer.

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Answers

Answer:

$37.8125

Step-by-step explanation:

$2.75 x 12.5 = 34.375

34.375 x 10% = 3.4375

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Answers

Answer:

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Step-by-step explanation:

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