A particle starts from rest and experiences constant acceleration for 6 s. If it travels a distance d1 in the first two seconds, a distance d2 in the next two seconds and a distance d3 in the last two seconds, then

Question

A particle starts from rest and experiences constant acceleration for 6 s. If it travels a distance d1 in the first two seconds, a distance d2 in the next two seconds and a distance d3 in the last two seconds, then (A) d1: d2: d3=1: 1: 1 (B) d1: d2: d3=1: 2: 3 (C) d1: d2: d3=1: 3: 5 (D) d1: d2: d3=1: 5: 9

Tardigrade Admin · Accepted Answer

Let pardcle start from 0 and travels distance

d_{1} (O A), d_{2} (A B), d_{3} (BC)

. .
From equation of motion, we have

S = u t + \frac{1}{2} g t^{2}

where

u

is initial velocity,

t

- time and

g

acceleration due to gravity.
For

O A : t = 2 s, u = 0

d_{1} = \frac{1}{2} a (2)^{2} = 2 a

For

OB : r = 4 s, u = 0

∴ d_{2} = \frac{1}{2} a (4)^{2} = 8 a

For

OC : u = 0, t = 6 s

∴ S = \frac{1}{2} a (6)^{2} = 18 a

Distance in last

2 s = 18 a - 8 a = 10 a

∴ d_{1} : d_{2} : d_{3} = 2 a : 6 a : 10 a

d_{1} : d_{2} : d_{3} = 1 : 3 : 5

Q. A particle starts from rest and experiences constant acceleration for $6 s$ . If it travels a distance $d_{1}$ in the first two seconds, a distance $d_{2}$ in the next two seconds and a distance $d_{3}$ in the last two seconds, then

$d_{1} : d_{2} : d_{3} = 1 : 1 : 1$

$d_{1} : d_{2} : d_{3} = 1 : 2 : 3$

$d_{1} : d_{2} : d_{3} = 1 : 3 : 5$

$d_{1} : d_{2} : d_{3} = 1 : 5 : 9$

Q. A particle starts from rest and experiences constant acceleration for 6s. If it travels a distance d1​ in the first two seconds, a distance d2​ in the next two seconds and a distance d3​ in the last two seconds, then

d1​:d2​:d3​=1:1:1

d1​:d2​:d3​=1:2:3

d1​:d2​:d3​=1:3:5

d1​:d2​:d3​=1:5:9

Q. A particle starts from rest and experiences constant acceleration for $6 s$ . If it travels a distance $d_{1}$ in the first two seconds, a distance $d_{2}$ in the next two seconds and a distance $d_{3}$ in the last two seconds, then

$d_{1} : d_{2} : d_{3} = 1 : 1 : 1$

$d_{1} : d_{2} : d_{3} = 1 : 2 : 3$

$d_{1} : d_{2} : d_{3} = 1 : 3 : 5$

$d_{1} : d_{2} : d_{3} = 1 : 5 : 9$