Question

A particle is moving in a straight line with initial velocity u & uniform accleration f . if the sum of the distances travelled in Tth & ( T+1 )th sec is 100 cm , then find its velocity after T seconds in cm/s . explain in detail

Answer 1

The distance covered in 'T^th' second will be given as

s = u + (f/2).(2T - 1)

and

the distance covered in '(T+1)^th' second will be given as

s' = u + (f/2).[2(T+1) - 1]

and we are given

if the sum of the distances travelled in T^th & ( T+1)^th sec is 100 cm

so,

s + s' = 100 cm

or

u + (f/2).(2T - 1) + u + (f/2).[2(T+1) - 1] = 100 cm

or

2u + (f/2).[(2T - 1) + (2T + 2 - 1)] = 100

or

2u + (f/2).[4T] = 100

or

2u + 2fT = 100

or

u + fT = 50

now, we know that

final velocity is given as

v = u + at

or in this case

v = u + fT

so,

we get the final velocity as

v = 50 cm/s