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# The formula for calculating the final veloc- ity of a body, initially

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Math Expert
Joined: 02 Sep 2009
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The formula for calculating the final veloc- ity of a body, initially  [#permalink]

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22 Feb 2018, 21:00
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15% (low)

Question Stats:

82% (01:33) correct 18% (01:45) wrong based on 61 sessions

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The formula for calculating the final velocity of a body, initially at rest, that undergoes a constant acceleration is v^2 = 2ad; where v is final velocity, a is acceleration, and d is distance traveled. If a body initially at rest is subjected to a constant acceleration of 10 meters/second^2 until it reaches a velocity of 20 meters/second, how far, expressed in meters, has the body traveled?

(A) 200

(B) 100

(C) 40

(D) 20

(E) 10

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The formula for calculating the final veloc- ity of a body, initially  [#permalink]

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22 Feb 2018, 23:15
Bunuel wrote:
The formula for calculating the final velocity of a body, initially at rest, that undergoes a constant acceleration is v^2 = 2ad; where v is final velocity, a is acceleration, and d is distance traveled. If a body initially at rest is subjected to a constant acceleration of 10 meters/second^2 until it reaches a velocity of 20 meters/second, how far, expressed in meters, has the body traveled?

(A) 200

(B) 100

(C) 40

(D) 20

(E) 10

Substituting the values in the equation, we get the solution to this problem

Given:
$$v^2 = 2ad$$ -> $$d = \frac{v^2}{2a}$$
Here, v = 20 and a = 10

Therefore, the distance can be calculated using the formula $$\frac{v^2}{2a} = \frac{400}{2*10} = \frac{400}{20} =$$20(Option D)

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Re: The formula for calculating the final veloc- ity of a body, initially  [#permalink]

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23 Feb 2018, 00:49
Bunuel wrote:
The formula for calculating the final velocity of a body, initially at rest, that undergoes a constant acceleration is v^2 = 2ad; where v is final velocity, a is acceleration, and d is distance traveled. If a body initially at rest is subjected to a constant acceleration of 10 meters/second^2 until it reaches a velocity of 20 meters/second, how far, expressed in meters, has the body traveled?

(A) 200

(B) 100

(C) 40

(D) 20

(E) 10

We'll show a complementary approach to the above, useful especially if you get lost in the wordiness of the question.
This is an Alternative approach and uses the answers.

Let's say the median answer, (C), is correct.
Then v^2 = 2*a*d = 2*10*40 = 800 meaning that v is the square root of 800, more than 20.
Too much! Since (C) gave too large of an answer, we'll look for a smaller option.
Say (D) was correct. Then v^2 = 2*10*20 = 400 and v=20, as required.

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Re: The formula for calculating the final veloc- ity of a body, initially  [#permalink]

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23 Feb 2018, 01:54
Bunuel wrote:
The formula for calculating the final velocity of a body, initially at rest, that undergoes a constant acceleration is v^2 = 2ad; where v is final velocity, a is acceleration, and d is distance traveled. If a body initially at rest is subjected to a constant acceleration of 10 meters/second^2 until it reaches a velocity of 20 meters/second, how far, expressed in meters, has the body traveled?

(A) 200

(B) 100

(C) 40

(D) 20

(E) 10

given v =20
a= 10

d=?

d= v^2/2a = 20x20/2x10 =20

(D) imo
Re: The formula for calculating the final veloc- ity of a body, initially   [#permalink] 23 Feb 2018, 01:54
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