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A body moving with a constant acceleration has a displacement of 1 m in 3rd second and 15 m in 10th second. The initial velocity of the body is:a)4m/sb)2m/ sc)-4m/sd)-2m/s
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A body moving with a constant acceleration has a displacement of 1 m i...
Problem:

A body moving with a constant acceleration has a displacement of 1 m in 3rd second and 15 m in 10th second. The initial velocity of the body is:


  • a) 4m/s

  • b) 2m/s

  • c) -4m/s

  • d) -2m/s



Solution:

Given:


  • Displacement in the 3rd second, s3 = 1 m

  • Displacement in the 10th second, s10 = 15 m


Let's assume:


  • Initial velocity of the body, u

  • Acceleration of the body, a



Calculating acceleration:

We know that:


  • Displacement in nth second, sn = u(n-1) + 1/2 a(n-1)^2


Using this formula, we can calculate the acceleration:


  • For the 3rd second, s3 = u(3-1) + 1/2a(3-1)^2

  • 1 = 2u + 2a

  • 2u + 2a = 1

  • u + a = 1/2



  • For the 10th second, s10 = u(10-1) + 1/2a(10-1)^2

  • 15 = 9u + 1/2a(9)^2

  • 15 = 9u + 40.5a

  • u + 4.5a = 15/9 = 5/3


Now we have two equations with two variables, we can solve them simultaneously to find the values of u and a.


Solving equations:


  • u + a = 1/2

  • u + 4.5a = 5/3


Subtracting the first equation from the second:


  • 3.5a = 1/6

  • a = 1/21 m/s^2


Substituting the value of a in the first equation:


  • u + 1/21 = 1/2

  • u = 1/2 - 1/21 = 10/21 m/s



Answer:

Therefore, the initial velocity of the body is:


  • u = 10/21 m/s

  • Option (e) is not
Community Answer
A body moving with a constant acceleration has a displacement of 1 m i...
The formula for displacement in the nth second is given by s(nth)= u + a/2 (2n-1)
hence,
1=u + a/2(5)
1 - 5a/2 = u

15= u + a/2(19)
15 - 19a/2 = u

1-5a/2 = 15 - 19a/2
14a/2 = 14
7a = 14
a= 2 m/s2

u = 1 - 10/2
u = -4m/s
The correct option should be (c)
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