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The position of a particle along x- axis at time t is given by x=2 + t - 3 t×t. The displacement and the distance travelled in the interval;t=0 to t=1 are respectively correct answer: -2,2.1 how to solve?
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The position of a particle along x- axis at time t is given by x=2 + t...
X = 2 +t -3t^2 ---------(1)
differentiate wrt time
dx/dt = 1 -6t ----------(2)
again differentiate wrt time
d^2x/dt^2 = -6
hence, motion is retarding becoz d^2x/dt^2 < 0
let at t time velocity of particle is zero
e.g dx/dt = 0 = 1-6t = 1/6
at t = 1/6 velocity of particle is zero .
then particle moves in back direction at t = 1 sec
now,
displacement = final position - initial position = x(1) - x (0)
= 2 + 1 -3 - 2
= -2 m
distance = | x(1) - x (1/6) | + | x (1/6) - x(0) |
= | 2 + 1 -3 -(2 +1/6 -3/36 | + | 2 + 1/6 -3/36 - 2 |
=| -2 - 1/6 +1/12 | + | 2 +1/6 -1/12 -2 |
= | -2 -1/12 | + | 1 /12 |
= 2 + 1/12 + 1/12
= 2 + 1/6 = 13/6 m
4.5
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The position of a particle along x- axis at time t is given by x=2 + t...
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The position of a particle along x- axis at time t is given by x=2 + t...
Solution:
Given:
Position of the particle along the x-axis at time t is given by: x = 2t - 3t^2
To find:
1. Displacement in the interval t = 0 to t = 1.
2. Distance traveled in the interval t = 0 to t = 1.
1. Displacement:
Displacement is the change in position of the particle. To find the displacement, we need to calculate the position at t = 1 and t = 0, and then find the difference between them.
At t = 1:
x = 2(1) - 3(1)^2
= 2 - 3
= -1
At t = 0:
x = 2(0) - 3(0)^2
= 0 - 0
= 0
Displacement = x(t = 1) - x(t = 0)
= (-1) - (0)
= -1
Therefore, the displacement in the interval t = 0 to t = 1 is -1.
2. Distance Traveled:
Distance traveled is the total length of the path covered by the particle. It can be calculated by taking the absolute value of the displacement.
Distance traveled = |Displacement|
= |-1|
= 1
Therefore, the distance traveled in the interval t = 0 to t = 1 is 1.
Summary:
- Displacement in the interval t = 0 to t = 1 is -1.
- Distance traveled in the interval t = 0 to t = 1 is 1.
Given:
Position of the particle along the x-axis at time t is given by: x = 2t - 3t^2
To find:
1. Displacement in the interval t = 0 to t = 1.
2. Distance traveled in the interval t = 0 to t = 1.
1. Displacement:
Displacement is the change in position of the particle. To find the displacement, we need to calculate the position at t = 1 and t = 0, and then find the difference between them.
At t = 1:
x = 2(1) - 3(1)^2
= 2 - 3
= -1
At t = 0:
x = 2(0) - 3(0)^2
= 0 - 0
= 0
Displacement = x(t = 1) - x(t = 0)
= (-1) - (0)
= -1
Therefore, the displacement in the interval t = 0 to t = 1 is -1.
2. Distance Traveled:
Distance traveled is the total length of the path covered by the particle. It can be calculated by taking the absolute value of the displacement.
Distance traveled = |Displacement|
= |-1|
= 1
Therefore, the distance traveled in the interval t = 0 to t = 1 is 1.
Summary:
- Displacement in the interval t = 0 to t = 1 is -1.
- Distance traveled in the interval t = 0 to t = 1 is 1.
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The position of a particle along x- axis at time t is given by x=2 + t - 3 t×t. The displacement and the distance travelled in the interval;t=0 to t=1 are respectively correct answer: -2,2.1 how to solve?
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The position of a particle along x- axis at time t is given by x=2 + t - 3 t×t. The displacement and the distance travelled in the interval;t=0 to t=1 are respectively correct answer: -2,2.1 how to solve? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position of a particle along x- axis at time t is given by x=2 + t - 3 t×t. The displacement and the distance travelled in the interval;t=0 to t=1 are respectively correct answer: -2,2.1 how to solve? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of a particle along x- axis at time t is given by x=2 + t - 3 t×t. The displacement and the distance travelled in the interval;t=0 to t=1 are respectively correct answer: -2,2.1 how to solve?.
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