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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?
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A particle moves along x-axis with acceleration a = 6(t− 1), where t i...
Given data:
- Initial velocity (Vo) = 2 m/s
- Acceleration (a) = 6(t - 1) m/s^2
Finding average acceleration:
Step 1: Calculate final velocity
- Given acceleration(a), we can find the velocity(v) at any time(t) using the formula:
v = u + at, where u is initial velocity
- At t = 10 sec:
v = 2 + ∫[6(t - 1)] dt (from t = 0 to t = 10)
v = 2 + 6∫(t - 1) dt
v = 2 + 6[(t^2/2) - t] (from 0 to 10)
v = 2 + 6[(100/2) - 10]
v = 2 + 6[50 - 10]
v = 2 + 6(40)
v = 2 + 240
v = 242 m/s
Step 2: Calculate average acceleration
- Average acceleration(a_avg) is given by:
a_avg = (v - u) / t
a_avg = (242 - 2) / 10
a_avg = 240 / 10
a_avg = 24 m/s^2
Therefore, the average acceleration of the particle from t = 0 to t = 10 sec is 24 m/s^2. Hence, the correct answer is (b) 24.
- Initial velocity (Vo) = 2 m/s
- Acceleration (a) = 6(t - 1) m/s^2
Finding average acceleration:
Step 1: Calculate final velocity
- Given acceleration(a), we can find the velocity(v) at any time(t) using the formula:
v = u + at, where u is initial velocity
- At t = 10 sec:
v = 2 + ∫[6(t - 1)] dt (from t = 0 to t = 10)
v = 2 + 6∫(t - 1) dt
v = 2 + 6[(t^2/2) - t] (from 0 to 10)
v = 2 + 6[(100/2) - 10]
v = 2 + 6[50 - 10]
v = 2 + 6(40)
v = 2 + 240
v = 242 m/s
Step 2: Calculate average acceleration
- Average acceleration(a_avg) is given by:
a_avg = (v - u) / t
a_avg = (242 - 2) / 10
a_avg = 240 / 10
a_avg = 24 m/s^2
Therefore, the average acceleration of the particle from t = 0 to t = 10 sec is 24 m/s^2. Hence, the correct answer is (b) 24.
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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?
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A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?.
A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves along x-axis with acceleration a = 6(t− 1), where t is in seconds. If the particle is initially at the origin and moves along positive x-axis with Vo 2 ms1, find average acceleration of particle from t = 0 to t = 10 sec. (a) 30 (b) 24 (c) 15 (d) 20?.
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