Initially, a particle is moving at 5.45 m/s at an angle of 38.5° above the horizontal. Four seconds later, its velocity is 6.24 m/s at an angle of 54.3° below the horizontal. What was the particle's average acceleration during these 4.00 seconds in the x-direction (enter first) and the y-direction?

V-Vo = 6.24/m/s[-54.3o]-5.45m/s[38.5o]

X = 6.24*Cos(-54.3) - 5.45*Cos38.5 = -0.624 m/s
Y = 6.24*sin(-54.3) - 5.45*sin38.5 = -8.46 m/s

ax = -0.624/4.0 = -0.156 m/s^2
ay = -8.46/4.0 = -2.115 m/s^2

Why did the particle take a detour? Because it can't seem to figure out which direction it wants to go!

But don't worry, I'm here to help. To calculate the particle's average acceleration in the x-direction, we need to find the change in velocity in the x-direction during the 4-second interval.

Initial velocity in the x-direction = 5.45 m/s * cos(38.5°)
Final velocity in the x-direction = 6.24 m/s * cos(-54.3°)

Now, to find the change in velocity in the x-direction, we subtract the initial velocity from the final velocity and divide by the time interval:

Change in velocity in the x-direction = (6.24 m/s * cos(-54.3°)) - (5.45 m/s * cos(38.5°)) / 4 s

As for the particle's average acceleration in the y-direction, we need to find the change in velocity in the y-direction during the 4-second interval.

Initial velocity in the y-direction = 5.45 m/s * sin(38.5°)
Final velocity in the y-direction = 6.24 m/s * sin(-54.3°)

To find the change in velocity in the y-direction, we subtract the initial velocity from the final velocity and divide by the time interval:

Change in velocity in the y-direction = (6.24 m/s * sin(-54.3°)) - (5.45 m/s * sin(38.5°)) / 4 s

So there you have it, the particle's average acceleration during these 4 seconds in the x-direction and the y-direction. Just plug in the values and let the math do its thing!

To find the particle's average acceleration in the x-direction, we need to calculate the change in the x-component of its velocity and divide it by the change in time.

Given:
Initial velocity (vx1) = 5.45 m/s
Angle with the horizontal (θ1) = 38.5°
Final velocity (vx2) = 6.24 m/s
Angle with the horizontal (θ2) = -54.3°
Change in time (Δt) = 4.00 s

First, let's calculate the initial x-component of the velocity:
vx1 = v1 * cos(θ1)
vx1 = 5.45 m/s * cos(38.5°)
vx1 = 4.25 m/s (rounded to 2 decimal places)

Next, let's calculate the final x-component of the velocity:
vx2 = v2 * cos(θ2)
vx2 = 6.24 m/s * cos(-54.3°)
vx2 = 3.02 m/s (rounded to 2 decimal places)

Now we can calculate the change in the x-component of velocity:
Δvx = vx2 - vx1
Δvx = 3.02 m/s - 4.25 m/s
Δvx = -1.23 m/s (rounded to 2 decimal places)

Finally, we can calculate the average acceleration in the x-direction:
Average acceleration in the x-direction (ax) = Δvx / Δt
ax = -1.23 m/s / 4.00 s
ax = -0.31 m/s² (rounded to 2 decimal places)

To find the particle's average acceleration in the y-direction, we need to calculate the change in the y-component of its velocity and divide it by the change in time.

First, let's calculate the initial y-component of the velocity:
vy1 = v1 * sin(θ1)
vy1 = 5.45 m/s * sin(38.5°)
vy1 = 3.34 m/s (rounded to 2 decimal places)

Next, let's calculate the final y-component of the velocity:
vy2 = v2 * sin(θ2)
vy2 = 6.24 m/s * sin(-54.3°)
vy2 = -4.98 m/s (rounded to 2 decimal places)

Now we can calculate the change in the y-component of velocity:
Δvy = vy2 - vy1
Δvy = -4.98 m/s - 3.34 m/s
Δvy = -8.32 m/s (rounded to 2 decimal places)

Finally, we can calculate the average acceleration in the y-direction:
Average acceleration in the y-direction (ay) = Δvy / Δt
ay = -8.32 m/s / 4.00 s
ay = -2.08 m/s² (rounded to 2 decimal places)

Therefore, the particle's average acceleration during these 4.00 seconds in the x-direction is -0.31 m/s² and in the y-direction is -2.08 m/s².

To find the average acceleration in the x-direction and y-direction, we need to consider the change in velocity in both the x and y components.

Given:
Initial velocity (magnitude) = 5.45 m/s
Initial angle = 38.5° above the horizontal
Final velocity (magnitude) = 6.24 m/s
Final angle = 54.3° below the horizontal
Time interval = 4.00 seconds

Step 1: Calculate the initial velocity components:
The x-component of the initial velocity is given by:
Vx_initial = V_initial * cos(θ_initial)

Substituting the given values:
Vx_initial = 5.45 m/s * cos(38.5°)

Step 2: Calculate the final velocity components:
The x-component of the final velocity is given by:
Vx_final = V_final * cos(θ_final)

Substituting the given values:
Vx_final = 6.24 m/s * cos(54.3°)

Step 3: Calculate the change in velocity in the x-direction:
ΔVx = Vx_final - Vx_initial

Step 4: Calculate the time interval:
Δt = 4.00 seconds

Step 5: Calculate the average acceleration in the x-direction:
ax = ΔVx / Δt

Now, let's calculate the average acceleration in the y-direction:

Step 6: Calculate the initial velocity components:
The y-component of the initial velocity is given by:
Vy_initial = V_initial * sin(θ_initial)

Substituting the given values:
Vy_initial = 5.45 m/s * sin(38.5°)

Step 7: Calculate the final velocity components:
The y-component of the final velocity is given by:
Vy_final = V_final * sin(θ_final)

Substituting the given values:
Vy_final = 6.24 m/s * sin(54.3°)

Step 8: Calculate the change in velocity in the y-direction:
ΔVy = Vy_final - Vy_initial

Step 9: Calculate the average acceleration in the y-direction:
ay = ΔVy / Δt

Now, plug in the appropriate values to calculate the average accelerations in the x and y directions.