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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.
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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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? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 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? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 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? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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