Question

A body moving with a uniform acceleration crosses a distance of 65 m in the 5th second and 105m in 9th second. How far will it go in 20s?

Answer 1

Answer:

2400m

Explanation:

Distance covered in nth second    Sn​=u+2a​(2n−1)

where  u and a are the initial velocity and acceleration respectively.

Case 1 :   Sn​=65       n=5

So,   65=u+2a​(2×5−1)

We get   65=u+4.5a            .....(1)

Case 2 :   Sn​=105       n=9

So,   105=u+2a​(2×9−1)

We get   105=u+8.5a            .....(2)

Equation (2) -(1),   40=4a

Or   a=10 m/s2

So,   65=u+4.5×10     ⟹ u=20 m/s

Distance covered in 20 seconds,   S=ut+21​at2

where t=20 s

S=20×20+21​(10)(20)2=2400 m