A body moves in a straight line with an acceleration 10m/s^2. If after 2 s it passes through O and after 3s it is 25 m from O, find its initial displacement relative to O.

Help thanks!! :)

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- Sep 5th 2006, 11:02 PMkolliBody
A body moves in a straight line with an acceleration 10m/s^2. If after 2 s it passes through O and after 3s it is 25 m from O, find its initial displacement relative to O.

Help thanks!! :) - Sep 5th 2006, 11:48 PMchanceyQuote:

Originally Posted by**kolli**

2. Does it change direction when it passes O?

3. What do you mean by initial displacement? - Sep 6th 2006, 12:32 AMCaptainBlackQuote:

Originally Posted by**kolli**

where is the initial velocity, and is the initial displacement.

RonL - Sep 6th 2006, 12:56 AMchanceyQuote:

Originally Posted by**CaptainBlack**

- Sep 6th 2006, 03:15 AMSoroban
Hello, kolli!

I'll assume this is a Calculus problem and you're familiar with integration.

Quote:

A body moves in a straight line with an acceleration

After 2s it passes through , and after 3s it is 25 m from .

Find its initial displacement relative to

I further assume that is the origin:

Let be the position function for the body.

Acceleration is the derivative of the velocity: .

. . Integrate: .

Velocity is the derivative of the position: .

. . Integrate: .

We are told that:

. . .**[1]**

We are told that:

. . .**[2]**

Subtract [1] from [2]: .

Substitute into [1]: .

Hence, the position function is: .

Therefore, at

. . Initially, the body was 20 meters "behind"

- Sep 6th 2006, 03:18 AMCaptainBlackQuote:

Originally Posted by**chancey**

,

and when , so:

.

These constitute a pair of simultaneous equations for and .

Solve these and you will have found the initial displacement (which

will be negative with the sign convention used here, change its sign if

you think that the questioner wanted it positive).

RonL - Sep 6th 2006, 05:54 AMtopsquarkQuote:

Originally Posted by**CaptainBlack**

*describe*s0 in those terms: The initial displacement was 20 m to the left of the origin.

-Dan - Sep 6th 2006, 06:05 AMCaptainBlackQuote:

Originally Posted by**topsquark**

acceleration to be +ve. Whether this is to the right or left is in a sense

irrelevant to us, it is in the direction of (if +ve) the acceleration or in the

opposite (if -ve) direction to the acceleration.

Maybe this is too sophisticated an idea for our posters, if so I will concede the

point :cool:

RonL - Sep 6th 2006, 06:10 AMtopsquarkQuote:

Originally Posted by**CaptainBlack**

-Dan