Question

The distance covered in n seconds and the distance covered in the nth second are different questions. Derive the equation for the distance covered in the nth second.

Answer 1

The distance covered in the nth second can be calculated using the formula S_nth = u + 1/2 × a × (2n-1), where S_nth is the distance covered in the nth second, u is the initial velocity, a is the acceleration, and n is the time in seconds.

Step-by-step explanation:

To determine the distance covered in the nth second by an object moving with uniform acceleration, we can use the equations of motion derived from kinematics. First, the total distance (S_n) covered in n seconds is given by the equation:
S_n = u × n + ½ × a × n^2
where u is the initial velocity, a is the acceleration, and n is the time in seconds. To find the distance covered specifically in the nth second (S_nth), we calculate the distance covered in n-1 seconds (S_{n-1}), subtract it from S_n, and obtain the distance for the nth second:

S_{n-1} = u × (n-1) + ½ × a × (n-1)^2

Therefore, the distance covered in the nth second is:
S_nth = S_n - S_{n-1}
Simplifying this gives us the formula:
S_nth = u + ½ × a × (2n-1)