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Particle is moving along path y=x2, from X=0m to X=2m, then distance travelled by the particle is
A)4m
B)8m
C)>√20m
D)?
A)4m
B)8m
C)>√20m
D)?
Most Upvoted Answer
Particle is moving along path y=x2, from X=0m to X=2m, then distance t...
Solution:
To find the total distance travelled by the particle, we need to calculate the length of the path followed by the particle from X=0m to X=2m.
We can do this by using the formula for the arc length of a curve, which is given by:
L = ∫[a,b] √(1 + (dy/dx)2) dx
where a and b are the limits of integration, dy/dx is the derivative of y with respect to x, and ∫ is the integral sign.
In this case, we have y = x2, so dy/dx = 2x. Substituting these values into the formula, we get:
L = ∫[0,2] √(1 + (2x)2) dx
To solve this integral, we can use a substitution, let u = 1 + (2x)2. Then du/dx = 4x, which means dx = du/4x. Substituting these values into the integral, we get:
L = ∫[1,5] √u du/(4x)
L = (1/4) ∫[1,5] u-1/2 du
L = (1/4) [2u1/2]1 5
L = (1/2) (√5 - 1)
Therefore, the distance travelled by the particle from X=0m to X=2m is √5 - 1 meters, which is approximately equal to 1.24 meters. Hence, the correct answer is option C) >√20m.
To find the total distance travelled by the particle, we need to calculate the length of the path followed by the particle from X=0m to X=2m.
We can do this by using the formula for the arc length of a curve, which is given by:
L = ∫[a,b] √(1 + (dy/dx)2) dx
where a and b are the limits of integration, dy/dx is the derivative of y with respect to x, and ∫ is the integral sign.
In this case, we have y = x2, so dy/dx = 2x. Substituting these values into the formula, we get:
L = ∫[0,2] √(1 + (2x)2) dx
To solve this integral, we can use a substitution, let u = 1 + (2x)2. Then du/dx = 4x, which means dx = du/4x. Substituting these values into the integral, we get:
L = ∫[1,5] √u du/(4x)
L = (1/4) ∫[1,5] u-1/2 du
L = (1/4) [2u1/2]1 5
L = (1/2) (√5 - 1)
Therefore, the distance travelled by the particle from X=0m to X=2m is √5 - 1 meters, which is approximately equal to 1.24 meters. Hence, the correct answer is option C) >√20m.
Community Answer
Particle is moving along path y=x2, from X=0m to X=2m, then distance t...
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Particle is moving along path y=x2, from X=0m to X=2m, then distance travelled by the particle isA)4mB)8mC)>√20mD)?
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