A particle is initially moving along the positive x-axis at a speed of 9.90 m/s. After 2.40 s, the particle is moving along the negative y-axis at a speed of 4.71 m/s. Find the x and y components of the particle's acceleration.
To find the x and y components of the particle's acceleration, we need to consider the change in velocity in both the x and y directions.
Given:
Initial velocity along the positive x-axis (Vix) = 9.90 m/s
Final velocity along the negative y-axis (Vfy) = -4.71 m/s
Time (t) = 2.40 s
To find the x component of acceleration (ax), we'll need to use the equation:
Vfx = Vix + ax * t
Since the particle is moving along the negative y-axis, the x-component of velocity (Vfx) would be zero.
0 = 9.90 m/s + ax * 2.40 s
To find the y component of acceleration (ay), we'll use the following equation:
Vfy = Viy + ay * t
Since the particle is moving along the negative y-axis, the initial velocity in the y-direction (Viy) would also be zero.
-4.71 m/s = 0 + ay * 2.40 s
Now, we can solve the two equations simultaneously to find the values of ax and ay.
From the first equation, we get:
ax = (0 - 9.90 m/s) / (2.40 s)
ax = -9.90 m/s / 2.40 s
ax = -4.13 m/s² (x component of acceleration)
From the second equation, we get:
ay = (-4.71 m/s) / (2.40 s)
ay = -1.96 m/s² (y component of acceleration)
Therefore, the x component of the particle's acceleration is -4.13 m/s², and the y component of the particle's acceleration is -1.96 m/s².