What time t does the particle first cross the x axis?

In summary, the conversation discusses a particle with an initial position and velocity, and a constant acceleration. The question asks for the time when the particle first crosses the x-axis and when it moves parallel to the y-axis. The second part of the conversation mentions an equation with a constant acceleration and difficulty understanding how to start the problem. The use of "i" and "j" is also mentioned.
  • #1
gap0063
65
0
1.
(a) A particle has ~r(0) = (4 m)j and ~v(0) =
(2 m/s)i.
If its acceleration is constant and given by
~a = −(2 m/s2) (i+j), at what time t does the
particle first cross the x axis?
Answer in units of s.

(b) At what time t is the particle moving parallel to the y axis; that is, in the j direction
Answer in units of s



2.Some equation with a constant acceleration... not sure which one



3. I tired to draw it out but I don't know how... I don't understand how to start the problem
 
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  • #2
Do you know what those i and j are?

ehild
 

Related to What time t does the particle first cross the x axis?

1. What is the equation for calculating the time at which a particle first crosses the x-axis?

The equation for calculating the time at which a particle first crosses the x-axis is t = -b/a, where t is the time, b is the y-intercept, and a is the velocity of the particle.

2. How do you determine the velocity of a particle in order to find the time at which it crosses the x-axis?

In order to determine the velocity of a particle, you can use the equation v = dx/dt, where v is the velocity, dx is the change in position, and dt is the change in time. This will give you the average velocity of the particle over a given time interval.

3. Can a particle cross the x-axis more than once?

Yes, a particle can cross the x-axis more than once. This will occur if the velocity of the particle changes direction and it travels back across the x-axis.

4. What factors can affect the time at which a particle crosses the x-axis?

The time at which a particle crosses the x-axis can be affected by the initial velocity, acceleration, and any external forces acting on the particle.

5. How can the concept of vectors be applied to determining the time at which a particle crosses the x-axis?

Vectors can be used to represent the direction and magnitude of the velocity and acceleration of a particle. By analyzing these vectors, you can determine the time at which the particle first crosses the x-axis.

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