Calculate the average velocity for a remote controlled vehicle that starts with a speed of 1.0 m/s [forward] and then accelerates at

0.08 m/s2 [backward] for 4.0 s.

Let forward be +, backward be -

vi = +1.0 m/s
a = -0.08 m/s²
t = 4.0 s
Δd = ?

d = vi(t)+1/2(a)(t²)
d = (1.0)(4.0)+1/2(-0.08)(4.0²)
Δd = 3.36 m

Now, using the definition of average velocity [which is *not* (vi+vf)/2]:
v_avg = Δd/Δt
v_avg = 3.36/4.0
v_avg = 0.84 m/s

vf=vi+at

a=-0.08 m/s²
vi=1 m/s
t=4 s

To calculate the average velocity, we need to find the total displacement and divide it by the total time.

Step 1: Find the initial velocity:
Given initial velocity (u) = 1.0 m/s [forward]

Step 2: Find the final velocity:
We need to find the final velocity (v) after accelerating for 4.0 seconds. Since the vehicle is accelerating backward, the final velocity will be less than the initial velocity.
Acceleration (a) = -0.08 m/s^2 [backward]
Time (t) = 4.0 s

Using the formula v = u + at, we can find the final velocity:
v = 1.0 m/s + (-0.08 m/s^2) * 4.0 s
v = 1.0 m/s - 0.32 m/s
v = 0.68 m/s [backward]

Step 3: Find the displacement:
Using the average velocity equation, average velocity (v_avg) = displacement / time

We can rearrange the equation to find the displacement:
displacement = v_avg * time

Since we want to find the average velocity and we know the final velocity and time, we can rearrange the equation to find the displacement:
displacement = v_avg * time
displacement = 0 * 4.0 s
displacement = 0 m

Step 4: Calculate the average velocity:
average velocity = displacement / time
average velocity = 0 m / 4.0 s
average velocity = 0 m/s

Therefore, the average velocity for the remote-controlled vehicle is 0 m/s.

To calculate the average velocity of the remote-controlled vehicle, we need to find the net displacement and divide it by the total time taken.

Step 1: Calculate the final velocity.
The vehicle starts with a speed of 1.0 m/s in the forward direction. Given that it accelerates at -0.08 m/s² for 4.0 s (backward acceleration), we can use the equation:

v = u + at

where:
v = final velocity
u = initial velocity
a = acceleration
t = time

Plugging in the values:
v = 1.0 m/s + (-0.08 m/s²)(4.0 s)
v = 1.0 m/s - 0.32 m/s
v = 0.68 m/s

So, the final velocity of the remote-controlled vehicle is 0.68 m/s in the forward direction.

Step 2: Calculate the average velocity.
The average velocity is given by the equation:

average velocity = total displacement / total time

Since the acceleration is not constant, we need to break down the motion into two parts - the initial motion with constant velocity and the motion during acceleration.

For the initial motion, the velocity remains constant at 1.0 m/s, and the displacement can be calculated using the equation:

displacement = initial velocity × time

displacement = 1.0 m/s × 4.0 s
displacement = 4.0 m

For the motion during acceleration, the velocity changes from 1.0 m/s to 0.68 m/s in 4.0 seconds. The displacement can be calculated using the equation:

displacement = (initial velocity + final velocity) × (time / 2)

displacement = (1.0 m/s + 0.68 m/s) × (4.0 s / 2)
displacement = 1.68 m/s × 2.0 s
displacement = 3.36 m

Now, we can calculate the total displacement by adding the displacements from the initial motion and motion during acceleration:

total displacement = displacement (initial motion) + displacement (motion during acceleration)
total displacement = 4.0 m + 3.36 m
total displacement = 7.36 m

Finally, we can calculate the average velocity:

average velocity = total displacement / total time
average velocity = 7.36 m / 4.0 s
average velocity ≈ 1.84 m/s

Therefore, the average velocity of the remote-controlled vehicle is approximately 1.84 m/s in the forward direction.