A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance s₁ in the first 10 seconds and distance s₂ in the next 10 seconds, then

• A. s₂ = s₁
• B. s₂ = 2s₁
• C. s₂ = 3s₁
• D. s₂ = 4s₁

To solve this problem, we can use the equations of motion under constant acceleration. When a particle starts from rest and accelerates, the distance traveled in a given time can be calculated using the formula:

Distance Formula

The distance \( s \) covered in time \( t \) is given by:

s = ut + (1/2)at²

Since the particle starts from rest, the initial velocity \( u = 0 \). Thus, the formula simplifies to:

s = (1/2)at²

Calculating Distances

Let's calculate the distances for the two intervals:

• For the first 10 seconds:

Using \( t = 10 \) seconds:

s₁ = (1/2)a(10)² = 50a

• For the next 10 seconds:

In the second interval (from 10 to 20 seconds), the total time is 20 seconds:

s₂ = (1/2)a(20)² - (1/2)a(10)² = (1/2)a(400 - 100) = (1/2)a(300) = 150a

Comparing Distances

Now, we can compare \( s₂ \) and \( s₁ \):

s₂ = 150a and s₁ = 50a

Thus, we find:

s₂ = 3s₁

Final Answer

The correct option is C. s₂ = 3s₁.