The velocity of a particle at the origin.

In summary, the conversation discusses finding the velocity of a particle at the origin using the position function x(t)=ct2+bt, where c=3m/s2 and b=-7m/s. The individual attempted to solve the problem by taking the derivative and setting t=0, but the answer was marked incorrect on the homework website. Other solutions were suggested, such as factoring out a t from the position equation and solving for t=0 or t=-b/c. Ultimately, the correct solution was found by solving for t=0 when x=0, which resulted in a velocity of 7m/s.
  • #1
MelissaJL
50
0

Homework Statement


A particle moves according to the position function x(t)=ct2+bt where c=3m/s2 and b=-7m/s. Find the velocity at the origin.


2. The attempt at a solution
I tried just taking the derivative and setting t=0 to the equation as so:
vx(t)=6t-7=6(0)-7=-7 m/s
Although, when I put the answer into WebAssign it says I'm incorrect. I'm not looking for a definite answer since this is my homework but would just like to understand what I am doing wrong.
 
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  • #2
Maybe they're looking for the velocity at the other time the particle is at the origin?
 
  • #3
I'm under the impression that the origin means they want me to solve it at t=0. What other origin could they be asking for?
 
  • #4
I guess they mean the origin of the coordinate system, i.e. x=0. You usually say t=0 rather than the slightly ominous "the origin of time".
 
  • #5
Yeah I just tried now to solve it at x=0 where I find that,
x(t)= 3t2-7t
0=3t2-7t+0constant
Then I treated it like a quadratic:
t=7+√[72-4(3)(9)] = 7/3s
2(3)
Then I put 7/3s into the formula...and...I got it right, thanks so much.



Answer ends like so,
vx=6(7/3)-7= 7m/s
 
  • #6
There is an easier way to solve it, just factor out one of the t's:
x=ct^2+bt = t(ct+b),
for which x=0 when t=0 or t=-b/c. Both solutions are of course valid (based on the problem text), even if the homework website doesn't think so...
 
  • #7
x(t) = 0 when t=2.3333333333
 

Related to The velocity of a particle at the origin.

1. What is the velocity of a particle at the origin?

The velocity of a particle at the origin refers to the rate of change of its position with respect to time when it is located at the origin, or point (0,0) on a coordinate system. It is typically measured in units of distance per time, such as meters per second.

2. How is the velocity of a particle at the origin calculated?

The velocity of a particle at the origin can be calculated by taking the derivative of its position function with respect to time. This can be written mathematically as v = dx/dt, where v represents velocity, x represents position, and t represents time.

3. Does the velocity of a particle at the origin change over time?

Yes, the velocity of a particle at the origin can change over time. This is because the particle's position is constantly changing, resulting in a change in its velocity. For example, if the particle is accelerating, its velocity will increase over time.

4. What factors can affect the velocity of a particle at the origin?

The velocity of a particle at the origin can be affected by several factors, including the particle's mass, the forces acting upon it, and any external factors such as friction or air resistance. Additionally, changes in the particle's position or acceleration can also impact its velocity.

5. How is the velocity of a particle at the origin used in scientific research?

The velocity of a particle at the origin is an important concept in many areas of scientific research, particularly in physics and engineering. It is often used to analyze and understand the motion of objects, such as projectiles or vehicles, and to make predictions about their behavior. It is also essential in the development of mathematical models and equations that describe the movement of particles and systems.

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