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!!
Hello, kolli!
I'll assume this is a Calculus problem and you're familiar with integration.
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"
You are told that when so: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
Since the original question was asking for a displacement, which is a vector, probably the best thing to do would be to define a positive direction (say, to the right), and describe s0 in those terms: The initial displacement was 20 m to the left of the origin.Originally Posted by CaptainBlack
-Dan
The sign convention (sense of the vectors) is implicit defined by taking theOriginally 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
RonL
Actually, no, I agree with you completely. Typically in any Physics I class students are taught to use what I call the "1-D vector notation" to describe vectors. I just wanted to point out the vector nature of the answer to highlight that the displacement is, in fact, a vector which students tend to forget about rather quickly. My last post was an example of me being (slightly) anal about the solution statement.Originally Posted by CaptainBlack
-Dan