A body is moving with uniform acceleration describe 40m in first 5second and 65m in next 5second. It's initial velocity will be?

5v + a/2 * 5^2 = 40 ____ (i)

10v + a/2 * 10^2 = 10^2 ____ (ii)
for (i) :
80 = 10v +25a
16 = 2v +5a _____ (a)
for (ii) :
105 = 10v + 100a/2
105 = 10v + 50a
21 = 2a + 10a _____ (b)
solve for( a )&( b )
we get ,
5a = 5
a=1
therefore :
2v +5=16
2v = 11
v = 5.5m/s

You have

5v + a/2 * 5^2 = 40
10v + a/2 * 10^2 = 105

Now just solve for v.

If initial velocity be u and the acceleration be a then the distance in first 5s will be S

5

=u(5)+
2
a(5)
2


=40m........(1)
and the distance in first 10s will be S
10

=u(10)+
2
a(10)
2



so the distance between time t=5s to t=10 will be
S
5


=S
10

−S
5

=65m ...........(2)
putting corresponding values and solving the equation-1 and equation-2 we get u=5.5m/s
Option C is correct.

To find the initial velocity of the body, we can use the equation of motion:

\[s = ut + \frac{1}{2}at^2\]

where:
- s is the displacement (distance traveled),
- u is the initial velocity,
- t is the time, and
- a is the acceleration.

From the information given, we know that the body travels a distance of 40m in the first 5 seconds and a distance of 65m in the next 5 seconds. Let's use this information to find the acceleration first.

For the first 5 seconds:
\[s_1 = 40m\]
\[t_1 = 5s\]

Using the equation of motion, we can write:
\[s_1 = ut_1 + \frac{1}{2}at_1^2\]

Plugging in the values we have:
\[40 = u(5) + \frac{1}{2}a(5)^2\]
\[40 = 5u + 12.5a \quad (equation 1)\]

Now, for the next 5 seconds:
\[s_2 = 65m\]
\[t_2 = 5s\]

Using the equation of motion again, we get:
\[s_2 = u(t_2) + \frac{1}{2}a(t_2)^2\]

Plugging in the values:
\[65 = u(5) + \frac{1}{2}a(5)^2\]
\[65 = 5u + 12.5a \quad (equation 2)\]

We now have a system of two equations (equation 1 and equation 2) with two unknowns (u and a). We can solve this system to find the values of u and a.

Subtracting equation 1 from equation 2, we get:
\[65 - 40 = 5u + 12.5a - 5u - 12.5a\]
\[25 = 0\]

This implies that there is no solution to this system of equations. It means that there is an inconsistency in the given data. Therefore, we cannot determine the initial velocity of the body with the information provided.

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