Question

A body covers 12m in 2nd second and 20 metre in 4th second how much distance will it cover in 4 seconds after the 5th second?

Answer 1

Case I:

Let initial velocity = u m/s

distance (s) = 12m

Time (t) = 2sec

S = u + a(2t - 1)/2

12 = u + (2 x 2 - 1)/2

12 = u + 3a/2

2u + 3a = 24--------------(1)

Case II:

Time(t) = 4 sec

distance(s) = 20 m

20 = u + a(2 x 4 - 1)/2

20 = u + 7a/2

2u + 7a = 40 --------(2)

from 1 and 2:

2u + 3a = 24

2u + 7a = 40

-      -     -
***********

-4a = -16

a = 4m/s²

Substitute the value of a in equation 1 we get :

u = 6 m/s 

Case iii:

Now, distance covered in 4 sec after 5 sec = distance covered in 9th sec-distance covered in 5 sec

= (6 x 9 + 1/24 x 9 x 9) - (6 x 5 + 1/2 x 4 x 5 x 5)

= 54 + 162 - (30 + 50)

= 136m