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An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.?
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An object is moving in a straight line with velocity v(t)=t×t-2t ms-1....
Ans is 0 bt here displacement is zero distance can't so in question displacement would be asked.
Community Answer
An object is moving in a straight line with velocity v(t)=t×t-2t ms-1....
Given:
The velocity of the object is given by v(t) = t^2 - 2t ms^-1.
To find:
The distance traveled by the object from t = 0 to t = 3 seconds.
Approach:
To find the distance traveled by the object, we need to integrate the velocity function with respect to time. The integral of velocity gives us the displacement, and taking the absolute value of the displacement gives us the distance.
Solution:
1. Calculate the antiderivative of the velocity function v(t):
∫(t^2 - 2t) dt = (1/3)t^3 - t^2 + C
2. To find the constant of integration (C), we use the initial condition that the object starts from the origin at t = 0. Therefore, we substitute t = 0 into the antiderivative:
(1/3)(0)^3 - (0)^2 + C = 0
C = 0
3. Now we have the displacement function:
d(t) = (1/3)t^3 - t^2
4. To find the distance traveled, we take the absolute value of the displacement function:
|d(t)| = |(1/3)t^3 - t^2|
5. Evaluate the distance function from t = 0 to t = 3 seconds:
|d(t)| = |(1/3)(3)^3 - (3)^2|
= |(1/3)(27) - 9|
= |9 - 9|
= 0
Answer:
The distance traveled by the object from t = 0 to t = 3 seconds is 0 units. This means that the object has returned to the origin after 3 seconds.
The velocity of the object is given by v(t) = t^2 - 2t ms^-1.
To find:
The distance traveled by the object from t = 0 to t = 3 seconds.
Approach:
To find the distance traveled by the object, we need to integrate the velocity function with respect to time. The integral of velocity gives us the displacement, and taking the absolute value of the displacement gives us the distance.
Solution:
1. Calculate the antiderivative of the velocity function v(t):
∫(t^2 - 2t) dt = (1/3)t^3 - t^2 + C
2. To find the constant of integration (C), we use the initial condition that the object starts from the origin at t = 0. Therefore, we substitute t = 0 into the antiderivative:
(1/3)(0)^3 - (0)^2 + C = 0
C = 0
3. Now we have the displacement function:
d(t) = (1/3)t^3 - t^2
4. To find the distance traveled, we take the absolute value of the displacement function:
|d(t)| = |(1/3)t^3 - t^2|
5. Evaluate the distance function from t = 0 to t = 3 seconds:
|d(t)| = |(1/3)(3)^3 - (3)^2|
= |(1/3)(27) - 9|
= |9 - 9|
= 0
Answer:
The distance traveled by the object from t = 0 to t = 3 seconds is 0 units. This means that the object has returned to the origin after 3 seconds.
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An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.?
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An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.? 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 An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.?.
An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.? 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 An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is moving in a straight line with velocity v(t)=t×t-2t ms-1. If it starts from the origin at t = 0 then find the distance of the object in t-0 to t = 3 second.?.
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