A Particle moving with uniform acceleration is found to travel 35m in the 8th second and 51m in the 9th second. its velocity in m/sec at the beginning of 11 seconds is
a> 49
b> 45
c> 47
d> 51
option 2
To find the velocity of the particle at the beginning of the 11th second, we first need to understand the motion of the particle.
Given that the particle has uniform acceleration, we can use the equations of motion to determine its velocity at different time intervals.
The distances traveled in the 8th and 9th seconds can be used to find the acceleration of the particle.
Let's denote the initial velocity of the particle as 'u' and the acceleration as 'a'.
Using the equation of motion for distance covered in time (s = ut + (1/2)at^2), we can substitute the given values:
For the 8th second:
35 = u*8 + (1/2)*a*8^2
For the 9th second:
51 = u*9 + (1/2)*a*9^2
Now, we have two equations with two unknowns (u and a). We can solve these equations simultaneously to find the values of u and a.
From the first equation, we get:
35 = 8u + 32a (Equation 1)
From the second equation, we get:
51 = 9u + 40.5a (Equation 2)
To solve these equations, we can multiply both sides of Equation 1 by 9 and Equation 2 by 8 to eliminate the 'u' term:
315 = 72u + 288a (Equation 3)
408 = 72u + 324a (Equation 4)
Subtracting Equation 3 from Equation 4, we get:
408 - 315 = 324a - 288a
93 = 36a
Divide both sides by 36:
a = 93/36
a ≈ 2.58 m/s^2
Now that we have the value of acceleration, we can substitute it into Equation 1 to find the value of 'u':
35 = 8u + 32(2.58)
35 - 32(2.58) = 8u
35 - 82.56 = 8u
-47.56 = 8u
u ≈ -5.95 m/s (initial velocity)
To find the velocity at the beginning of the 11th second, we can use the equation for velocity at time (v = u + at):
v = -5.95 + 2.58(11-0)
v = -5.95 + 2.58(11)
v = -5.95 + 28.38
v ≈ 22.43 m/s
Therefore, the velocity of the particle at the beginning of the 11th second is approximately 22.43 m/s.
None of the given options (a, b, c, d) match this value, so none of them are correct.