Question

A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals
of 4 sec each. Its initial velocity is -
(A)
1 m/sec
(B)
10 m/sec
5 m/sec
(D)
2 m/sec​

Answer 1

Answer:

A. 1 m/s

Explanation:

Formula to be used

s = ut + 1/2*a*t²

there are 2 intervals of 4 and 4 sec, therefore the total journey can be summed up as

1.First journey of 4 sec

2.the other one of 8 sec (4+4=8)

Total distance traveled in the two journey:

1.For the first journey its 24 m

2.for the second journey its 24 + 64 = 88 m

Let the acceleration be 'a' and initial velocity be 'u'

Since we now have everything therefore we can freely write the equation of motion.

For the first journey

24 = u*4 + 1/2*a*4² ------------------ 1

For the second journey

88 = u*8 + 1/2*a*8² --------------------- 2

we have two equations and two variables.

(Solving the two equations by elimination method)

Multiplying equation 1 by 4 and

96 = u*4*4+1/2*a*16*4  -------------------- 3

(Subtracting equation 2 from equation 3)

we get

96-88 = 16u - 8u + 1/2*a*64 - 1/2*a*64

8=8u

u=1 m/s

Hope this helps.