A particle leaves its orgin with a velocity of 4 i m/s and a constant acceleration of (-2i + .5j) m/s^2. At the time the particle reaches its maximum X corrdinate a) what is its velocity? b) what is its position vector?
I'm not sure which equations i should use.
solve for the max x coordinate:
dx= vi*t +1/2 at^2
dx/dt=0=vi + at
t= -vi/a
now, solve for velocity and position at that time.
To solve for the maximum X coordinate, we can use the equation:
dx = vi * t + 1/2 * a * t^2
Where:
- dx represents the change in position along the X axis.
- vi represents the initial velocity.
- a represents the constant acceleration.
- t represents the time.
In this case, vi = 4i m/s (as given in the question) and a = (-2i + 0.5j) m/s^2. We need to find the time at which the particle reaches its maximum X coordinate.
To find the time, we can use the equation:
0 = vi + at
Substituting the given values:
0 = 4i + (-2i + 0.5j) * t
Simplifying this equation will give us the time (t) at which the particle reaches its maximum X coordinate.
Once we have the time (t), we can use it to find the values of velocity and position at that time.
a) To find the velocity, we can use the equation:
v = vi + at
Substituting the values of vi, a, and the obtained value of t will give us the velocity at that time.
b) To find the position vector, we can use the equation:
r = ri + vi * t + (1/2) * a * t^2
Where r represents the position vector.
Substituting the values of ri (which is the origin), vi, a, and the obtained value of t will give us the position vector at that time.