Question

A particle is moving in straight line with initial velocity u and uniform acceleration a. If the sum of the distances travelled tth and (t+1)th seconds 100cm, then its velocity after t seconds in cm/s is?

A. 20
B. 30
C. 50
D. 80

Answer 1

According to formula,
S = u + 0.5a(2n-1)
nth
where 'n' is nth second.

Answer 2

Answer:

C) 50

Explanation:

Distance travelled in nth second of uniformly accelerated motion =

Sn = u+a/2(2n-1)

where u is the initial velocity and a the uniform acceleration of the body.

The sum of distances travelled in T th & (T+1) th second = 100 cm

Therefore,

ST +ST+1 =100

If the particle is moving with initial velocity U and uniform acceleration A, distance travelled by the particle in Tth second will be -

100 = s(t-th) + s(t+1th)

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

100 = 2u + a(2t - 1)/2 + a(2t + 1)/2

100 = 2u + (a/2)(2t - 1 + 2t + 1)

100 = 2u + (a/2)(4t)

100 = 2u + a(2t)

100 = 2u + 2at

100 = 2(u + at)

50 = u + at

50 = v

Therefore, the velocity after t seconds is 50cm/s.