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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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