Question::

A body travelling in straight line travels 2m in the first two seconds and 2.2m in next four seconds with consttant retardation. what will be the velocity at the end of the seventh second from the start?

To determine the velocity of the body at the end of the seventh second, we first need to analyze the motion described in the problem. The body travels a total distance of 2 meters in the first two seconds and 2.2 meters in the next four seconds, indicating that it is experiencing constant retardation. Let's break this down step by step.

Understanding the Motion

The motion can be divided into two segments:

• First segment: 0 to 2 seconds, where the distance covered is 2 meters.
• Second segment: 2 to 6 seconds, where the distance covered is 2.2 meters.

Calculating Average Velocities

To find the average velocity during each segment, we can use the formula:

Average Velocity = Total Distance / Total Time

For the first segment (0 to 2 seconds):

Average Velocity (V1) = 2 m / 2 s = 1 m/s

For the second segment (2 to 6 seconds):

Average Velocity (V2) = 2.2 m / 4 s = 0.55 m/s

Finding Initial and Final Velocities

Since the body is decelerating, we can denote the initial velocity at the start of the first segment as u and the final velocity at the end of the sixth second as v.

Using the average velocities, we can express them in terms of initial and final velocities:

• For the first segment: V1 = (u + v1) / 2 = 1 m/s
• For the second segment: V2 = (v1 + v) / 2 = 0.55 m/s

Setting Up the Equations

From the first segment:

u + v1 = 2 m/s (1)

From the second segment:

v1 + v = 1.1 m/s (2)

Solving the Equations

Now we can solve these two equations to find the values of u, v1, and v.

From equation (1):

v1 = 2 - u (3)

Substituting equation (3) into equation (2):

(2 - u) + v = 1.1

v = 1.1 - (2 - u)

v = u - 0.9 (4)

Using the Retardation Concept

Since the body is decelerating, we can find the retardation using the average velocities:

a = (v - u) / t

For the entire time of 6 seconds, we can express the average velocity:

Average Velocity = (u + v) / 2 = (1 + 0.55) / 2 = 0.775 m/s

Thus, we can find the final velocity at the end of the seventh second:

v = u - 0.9

Calculating the Final Velocity

We know that the body has been decelerating, and we can find the final velocity after 7 seconds using the average velocity over the total time:

v = u - 0.9

Now, we can substitute the values we have derived:

At the end of the seventh second, the velocity will be:

v = 1 - 0.9 = 0.1 m/s

Final Result

Therefore, the velocity of the body at the end of the seventh second is 0.1 m/s.