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A particle in one dimensional motion with uniform acceleration along straight. It travels a distance of 24m in the 1st 2s and 95m in the next 5s. Calculate its initial velocity and uniform acceleration of the particle?
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A particle in one dimensional motion with uniform acceleration along s...
Given:
Distance traveled in the first 2 seconds, d1 = 24 m
Distance traveled in the next 5 seconds, d2 = 95 m

To Find:
Initial velocity, u
Uniform acceleration, a

Formula:
The equation of motion for a particle with uniform acceleration is given by:
s = ut + (1/2)at^2
where s is the displacement, u is the initial velocity, a is the uniform acceleration, and t is the time.

Calculation:

Step 1: Calculate the displacement in the first 2 seconds using the equation of motion:
24 = u(2) + (1/2)a(2)^2
24 = 2u + 2a ------(1)

Step 2: Calculate the displacement in the next 5 seconds using the equation of motion:
95 = u(5) + (1/2)a(5)^2
95 = 5u + 12.5a ------(2)

Step 3: Solve the system of equations (1) and (2) to find the values of u and a.

Multiplying equation (1) by 5 and equation (2) by 2, we get:

120 = 10u + 10a ------(3)
190 = 10u + 25a ------(4)

Subtracting equation (3) from equation (4):

190 - 120 = 10u + 25a - 10u - 10a
70 = 15a

Dividing both sides by 15:

70/15 = a
a = 4.67 m/s^2

Substituting the value of a into equation (3):

120 = 10u + 10(4.67)
120 = 10u + 46.7

Rearranging the equation:

10u = 120 - 46.7
10u = 73.3

Dividing both sides by 10:

u = 7.33 m/s

Answer:
The initial velocity of the particle is 7.33 m/s and the uniform acceleration is 4.67 m/s^2.
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A particle in one dimensional motion with uniform acceleration along straight. It travels a distance of 24m in the 1st 2s and 95m in the next 5s. Calculate its initial velocity and uniform acceleration of the particle?
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