A body moving with acceleration covers a displacement of 5m in 2. Find the velocity after 2s if its initial velocity is 1m/s

To find the final velocity of a body moving with acceleration after a certain displacement, we can use the equations of motion. In this case, we know the initial velocity, the displacement, and the time taken. Let's break it down step by step.

Given Information

• Initial Velocity (u): 1 m/s
• Displacement (s): 5 m
• Time (t): 2 s

Using the Equations of Motion

We can use the second equation of motion, which relates displacement, initial velocity, time, and acceleration:

s = ut + (1/2)at²

Here, we need to find the acceleration (a) first. We can rearrange the equation to solve for acceleration:

a = (2(s - ut)) / t²

Calculating Acceleration

Substituting the known values into the equation:

a = (2(5 m - (1 m/s)(2 s))) / (2 s)²

First, calculate the term inside the parentheses:

5 m - 2 m = 3 m

Now plug this back into the equation:

a = (2(3 m)) / 4 s² = 6 m / 4 s² = 1.5 m/s²

Finding Final Velocity

Now that we have the acceleration, we can find the final velocity (v) using the first equation of motion:

v = u + at

Substituting the values:

v = 1 m/s + (1.5 m/s²)(2 s)

Calculating the second term:

1.5 m/s² * 2 s = 3 m/s

Now, add this to the initial velocity:

v = 1 m/s + 3 m/s = 4 m/s

Final Result

After 2 seconds, the final velocity of the body is 4 m/s.

This method illustrates how we can systematically apply the equations of motion to find unknown quantities when we have certain initial conditions. If you have any further questions or need clarification on any step, feel free to ask!