Object moves distance in ratio 1:3:4. Find average velocity( v​₁, v​​​₂, v_{3 )}

To find the average velocity of an object that moves distances in the ratio of 1:3:4, we need to first understand what average velocity is. Average velocity is defined as the total displacement divided by the total time taken. In this case, we can break down the problem into manageable steps.

Understanding the Distances

Let’s denote the distances moved in each segment as follows:

• Distance 1 (d1) = 1 unit
• Distance 2 (d2) = 3 units
• Distance 3 (d3) = 4 units

Now, if we add these distances together, we get the total distance:

Total Distance (D) = d1 + d2 + d3 = 1 + 3 + 4 = 8 units

Considering Time for Each Segment

Next, we need to consider the time taken for each segment of the journey. Let’s assume the velocities for each segment are:

• Velocity 1 (v1)
• Velocity 2 (v2)
• Velocity 3 (v3)

The time taken for each segment can be calculated using the formula:

Time = Distance / Velocity

Thus, the times for each segment would be:

• Time 1 (t1) = d1 / v1 = 1 / v1
• Time 2 (t2) = d2 / v2 = 3 / v2
• Time 3 (t3) = d3 / v3 = 4 / v3

Calculating Total Time

The total time (T) taken for the entire journey is the sum of the times for each segment:

Total Time (T) = t1 + t2 + t3 = (1 / v1) + (3 / v2) + (4 / v3)

Finding Average Velocity

Now, we can find the average velocity (V_avg) using the formula:

Average Velocity (V_avg) = Total Distance / Total Time

Substituting the values we have:

V_avg = D / T = 8 / [(1 / v1) + (3 / v2) + (4 / v3)]

Final Expression

So, the average velocity of the object moving in the ratio of 1:3:4, given its velocities for each segment, can be expressed as:

V_avg = 8 / [(1 / v1) + (3 / v2) + (4 / v3)]

This formula allows you to calculate the average velocity once you know the specific velocities for each segment of the journey. If you have particular values for v1, v2, and v3, you can substitute them into this equation to find the average velocity.