A body moves with

2m/s2

acceleration after starting from rest.The distance covered in the

5th

second is

To find the distance covered by a body in the 5th second when it starts from rest and accelerates at 2 m/s², we can use the equations of motion. Specifically, we will focus on the formula that helps us determine the distance covered during a specific second of motion.

Understanding the Motion

When an object accelerates from rest, its initial velocity (u) is 0. The acceleration (a) is given as 2 m/s². We want to calculate the distance covered in the 5th second, which requires us to first understand how distance is calculated in uniformly accelerated motion.

Key Formula

The distance covered in the nth second can be calculated using the formula:

• S_n = u + (1/2) a (2n - 1)

Where:

• S_n = distance covered in the nth second
• u = initial velocity (0 m/s in this case)
• a = acceleration (2 m/s²)
• n = the second for which we want to find the distance (5 in this case)

Calculating the Distance

Now, substituting the values into the formula:

• u = 0 m/s
• a = 2 m/s²
• n = 5

Plugging these values into the formula:

• S₅ = 0 + (1/2) * 2 * (2 * 5 - 1)
• S₅ = 0 + (1/2) * 2 * (10 - 1)
• S₅ = (1) * 9
• S₅ = 9 meters

Final Result

Thus, the distance covered in the 5th second is 9 meters. This method allows us to pinpoint the distance traveled during any specific second of motion, which is particularly useful in problems involving uniform acceleration.