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A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s?
Most Upvoted Answer
A particle starts with an initial velocity 2.5m/s along the +ve x axis...
Given:
Initial velocity (u) = 2.5 m/s
Acceleration (a) = 0.5 m/s²
(a) Distance traveled in the first two seconds:
We can use the kinematic equation to find the distance traveled by the particle in the first two seconds.
The kinematic equation is:
s = ut + 0.5at²
Substituting the given values:
s = (2.5 m/s)(2 s) + 0.5(0.5 m/s²)(2 s)²
s = 5 m + 0.5 m/s² * 4 s²
s = 5 m + 0.5 m/s² * 16 s²
s = 5 m + 8 m
s = 13 m
Therefore, the particle travels a distance of 13 meters in the first two seconds.
(b) Time taken to reach a velocity of 7.5 m/s:
We can use the equation of motion to find the time taken to reach a velocity of 7.5 m/s.
The equation of motion is:
v = u + at
Substituting the given values:
7.5 m/s = 2.5 m/s + 0.5 m/s² * t
Rearranging the equation to solve for t:
7.5 m/s - 2.5 m/s = 0.5 m/s² * t
5 m/s = 0.5 m/s² * t
t = 5 m/s / 0.5 m/s²
t = 10 s
Therefore, it takes 10 seconds for the particle to reach a velocity of 7.5 m/s.
(c) Distance covered before reaching a velocity of 7.5 m/s:
To find the distance covered before reaching a velocity of 7.5 m/s, we can use the equation of motion.
The equation of motion is:
v² = u² + 2as
Substituting the given values:
(7.5 m/s)² = (2.5 m/s)² + 2(0.5 m/s²)s
Simplifying the equation:
56.25 m²/s² = 6.25 m²/s² + 1 m/s² * s
56.25 m²/s² - 6.25 m²/s² = 1 m/s² * s
50 m²/s² = 1 m/s² * s
s = 50 m²/s² / 1 m/s²
s = 50 m
Therefore, the particle will cover a distance of 50 meters before reaching a velocity of 7.5 m/s.
In summary,
(a) The particle travels a distance of 13 meters in the first two seconds.
(b) It takes 10 seconds for the particle to reach a velocity of 7.5 m/s.
(c) The particle will cover a distance of 50 meters before reaching a velocity of 7.5 m/s.
Initial velocity (u) = 2.5 m/s
Acceleration (a) = 0.5 m/s²
(a) Distance traveled in the first two seconds:
We can use the kinematic equation to find the distance traveled by the particle in the first two seconds.
The kinematic equation is:
s = ut + 0.5at²
Substituting the given values:
s = (2.5 m/s)(2 s) + 0.5(0.5 m/s²)(2 s)²
s = 5 m + 0.5 m/s² * 4 s²
s = 5 m + 0.5 m/s² * 16 s²
s = 5 m + 8 m
s = 13 m
Therefore, the particle travels a distance of 13 meters in the first two seconds.
(b) Time taken to reach a velocity of 7.5 m/s:
We can use the equation of motion to find the time taken to reach a velocity of 7.5 m/s.
The equation of motion is:
v = u + at
Substituting the given values:
7.5 m/s = 2.5 m/s + 0.5 m/s² * t
Rearranging the equation to solve for t:
7.5 m/s - 2.5 m/s = 0.5 m/s² * t
5 m/s = 0.5 m/s² * t
t = 5 m/s / 0.5 m/s²
t = 10 s
Therefore, it takes 10 seconds for the particle to reach a velocity of 7.5 m/s.
(c) Distance covered before reaching a velocity of 7.5 m/s:
To find the distance covered before reaching a velocity of 7.5 m/s, we can use the equation of motion.
The equation of motion is:
v² = u² + 2as
Substituting the given values:
(7.5 m/s)² = (2.5 m/s)² + 2(0.5 m/s²)s
Simplifying the equation:
56.25 m²/s² = 6.25 m²/s² + 1 m/s² * s
56.25 m²/s² - 6.25 m²/s² = 1 m/s² * s
50 m²/s² = 1 m/s² * s
s = 50 m²/s² / 1 m/s²
s = 50 m
Therefore, the particle will cover a distance of 50 meters before reaching a velocity of 7.5 m/s.
In summary,
(a) The particle travels a distance of 13 meters in the first two seconds.
(b) It takes 10 seconds for the particle to reach a velocity of 7.5 m/s.
(c) The particle will cover a distance of 50 meters before reaching a velocity of 7.5 m/s.
Community Answer
A particle starts with an initial velocity 2.5m/s along the +ve x axis...
A) 6 meters b) 10 sec. c) 50 meters
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A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s?
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A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s? 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 starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s?.
A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s? 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 starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts with an initial velocity 2.5m/s along the +ve x axis and it accelerates uniformly at the rate 0.5m/ss. (a) find distance travelled by it in first two seconds. (b)How much time does it take to reach the velocity 7.5m/s (c)How much distance will it cover before reaching the velocity 7.5m/s?.
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