Aparticle 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

why?

The correct answer is D. s₂=4s₁

Explanation:

The distance of a particle is given by:

where

s₀ is the initial position when t=0

v₀ is the initial speed when t=0

a is the constant acceleration

t is the time in seconds

Then, the position s₁ is given by:

As the particle starts from rest v₀=0 and we consider s₀=0, s₁ will be:

Furthermore, the position s₂ is:

In this case t₁=10 s and t₂=20 s (10 seconds later). In other words t₂=2t₁.

We replace the value of  t₂ in the second equation (s₂):

Finally, we divide s₂ by s₁ to get the ratio: