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A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.?
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A body starts moving with an initial velocity of 10 m/s and moves alon...
Problem Statement: A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.
Solution:
To solve the problem, we need to use the equations of motion.
Step 1: Determine the acceleration of the particle before it changes direction.
Let the acceleration of the particle be a. We know that the velocity of the particle changes from 10m/s to 50m/s. Therefore, we can use the equation v = u + at to find the acceleration.
v = 50m/s (final velocity)
u = 10m/s (initial velocity)
t = unknown
v = u + at
50 = 10 + at
t = (50 - 10)/a
t = 40/a
Step 2: Determine the distance travelled by the particle before it changes direction.
We can use the equation s = ut + 1/2at^2 to find the distance travelled by the particle.
s = unknown
u = 10m/s (initial velocity)
t = 40/a (time taken to reach 50m/s)
a = a (acceleration)
s = ut + 1/2at^2
s = 10(40/a) + 1/2a(40/a)^2
s = 400/a + 800/a
s = 1200/a
Step 3: Determine the time taken by the particle to reach the starting point.
After the acceleration is reversed, the particle will travel the same distance as it did before. Therefore, the total distance travelled by the particle is 2s.
Total distance = 2s = 2400/a
Using the equation v^2 = u^2 + 2as, we can find the final velocity of the particle when it reaches the starting point.
v = unknown
u = 50m/s (final velocity before the acceleration is reversed)
a = -a (acceleration after the acceleration is reversed)
s = 2400/a (total distance travelled by the particle)
v^2 = u^2 + 2as
v^2 = 50^2 + 2(-a)(2400/a)
v^2 = 2500 - 4800
v^2 = -2300
Since the velocity cannot be negative, the particle does not reach the starting point. Therefore, the answer is zero.
Conclusion: The speed of the particle in m/s when it reaches the starting point is zero.
Solution:
To solve the problem, we need to use the equations of motion.
Step 1: Determine the acceleration of the particle before it changes direction.
Let the acceleration of the particle be a. We know that the velocity of the particle changes from 10m/s to 50m/s. Therefore, we can use the equation v = u + at to find the acceleration.
v = 50m/s (final velocity)
u = 10m/s (initial velocity)
t = unknown
v = u + at
50 = 10 + at
t = (50 - 10)/a
t = 40/a
Step 2: Determine the distance travelled by the particle before it changes direction.
We can use the equation s = ut + 1/2at^2 to find the distance travelled by the particle.
s = unknown
u = 10m/s (initial velocity)
t = 40/a (time taken to reach 50m/s)
a = a (acceleration)
s = ut + 1/2at^2
s = 10(40/a) + 1/2a(40/a)^2
s = 400/a + 800/a
s = 1200/a
Step 3: Determine the time taken by the particle to reach the starting point.
After the acceleration is reversed, the particle will travel the same distance as it did before. Therefore, the total distance travelled by the particle is 2s.
Total distance = 2s = 2400/a
Using the equation v^2 = u^2 + 2as, we can find the final velocity of the particle when it reaches the starting point.
v = unknown
u = 50m/s (final velocity before the acceleration is reversed)
a = -a (acceleration after the acceleration is reversed)
s = 2400/a (total distance travelled by the particle)
v^2 = u^2 + 2as
v^2 = 50^2 + 2(-a)(2400/a)
v^2 = 2500 - 4800
v^2 = -2300
Since the velocity cannot be negative, the particle does not reach the starting point. Therefore, the answer is zero.
Conclusion: The speed of the particle in m/s when it reaches the starting point is zero.
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A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.?
Question Description
A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.?.
A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body starts moving with an initial velocity of 10 m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50m/s the acceleration is reversed in direction without changing. Find the speed of the particle in m/s when it reaches the starting point.?.
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