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

Question

Answer

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

Answer

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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