the coordinates of a particle(m/s) in a plane at a given time(t),is 2t,t squared,determine of motion
To determine the motion of the particle, we need to find its velocity and acceleration.
The position of the particle at any given time t is given by the coordinates (2t, t^2).
First, let's find the velocity of the particle. Velocity is the rate of change of position with respect to time. We can find the velocity by taking the derivative of the position function:
Velocity, v(t) = (dx/dt, dy/dt)
The x-coordinate of the particle's position is 2t, so dx/dt = 2.
The y-coordinate of the particle's position is t^2, so dy/dt = 2t.
Therefore, the velocity v(t) = (2, 2t).
Next, let's find the acceleration of the particle. Acceleration is the rate of change of velocity with respect to time. We can find the acceleration by taking the derivative of the velocity function:
Acceleration, a(t) = (dv_x/dt, dv_y/dt)
The x-component of the velocity is constant, so dv_x/dt = 0.
The y-component of the velocity is 2t, so dv_y/dt = 2.
Therefore, the acceleration a(t) = (0, 2).
In summary, the motion of the particle is described by:
- Velocity: v(t) = (2, 2t)
- Acceleration: a(t) = (0, 2)
The particle is moving in a straight line with a constant velocity of 2 m/s in the x-direction and a constant acceleration of 2 m/s^2 in the y-direction.