Final answer:
To find the distance traveled in the nth second, you calculate the total distance up to the nth second and subtract the distance up to the (n-1)th second using the motion equations for constant acceleration.
Step-by-step explanation:
To derive the distance traveled in the nth second by an object moving with uniform acceleration, you can use the formula s = ut + ½at² where s is the total distance traveled, u is the initial velocity, t is the time, and a is the acceleration. To find the distance covered during the nth second, you need to calculate the distance traveled until the nth second and subtract the distance covered until the (n-1)th second.
Step 1: Calculate the distance (Sn) covered until the end of the nth second: Sn = u ⋅ n + ½ ⋅ a ⋅ n²
Step 2: Calculate the distance (Sn-1) covered until the end of the (n-1)th second: Sn-1 = u ⋅ (n-1) + ½ ⋅ a ⋅ (n-1)²
Step 3: Subtract Sn-1 from Sn to find the distance covered in the nth second: Distance in nth second = Sn - Sn-1
This method provides the distance an object travels in the nth second of its motion when it is experiencing constant acceleration.