Motion in a Straight Line

Step 1: Write the formula for distance in the n-th second
The distance a freely falling object travels during the n-th second is given by: Sn=u+‌

1

2

g(2n−1) Here, u is the starting speed (which is 0 if just falling), g is gravity, and n is the second we are looking at.
Step 2: Substitute the values
We know the speed at start u=0 and g=10ms−2. The distance in the last but one second is 5 m , so: 5=0+‌

1

2

×10(2n−1)
Step 3: Solve for n
Simplify the equation: 5=5(2n−1)⇒‌

5

5

=2n−1⇒1=2n−1⇒2n=2⇒n=1
This means the last but one second is the 1st second of the fall.