Question

An ant moved for several seconds and covered 3 mm in the first second and 4 mm more in each successive second than in its predecessor. If the ant had covered 1 mm in the first second and 8 m more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than 6 mm but less than 30 mm. Find the time for which the ant moved (in seconds)

Options

• 5 s

• 4 s

• 6 s

• None of these

Answer 1

4 s

Explanation:

Let ant move for t second

Case I :

S_t when ant move 3 m min first second and 4 m min in each second.

`"S"_"n"="t"/2[2(3)+("t"-1)4]`

Case II :

St when ant move 1 mm in the first second and 8 mm in each second

`"S"_"t"="t"/2[2("v")+("t"-1)8]`

ATQ,

`6<"t"/2[2+("t"-1)8]-"t"/2[6+("t"-1)4]<30`

`6<"t"/2[-8+4"t"]<30`

6 <[− 4t + 2t²]< 30

From option putting t = 4 Only condition is satisfied
6 < − 16 + 32 < 30

6 < 16 < 30