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A body begins at rest and accelerates uniformly to cover a distance of 6 metres. If its velocity after the displacement is 6 m/s, then its uniform acceleration a is
- a)6 m/s2
- b)2 m/s2
- c)3 m/s2
- d)4 m/s2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A body begins at rest and accelerates uniformly to cover a distance of...
We can use the kinematic equation to relate initial velocity (u), acceleration (a), distance (s), and final velocity (v):
v2 = u2 + 2as
In this case, the body begins at rest, so the initial velocity u is 0 m/s. The final velocity v is given as 6 m/s, and the distance s is 6 m. We want to find the acceleration a.
62 = 02 + 2a(6)
36 = 12a
a = 36/12
a = 3m/s2
So, the correct answer is (c) 3 m/s².
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Community Answer
A body begins at rest and accelerates uniformly to cover a distance of...
Acceleration is the rate of change of velocity with respect to time. In this problem, we are given that the body begins at rest and accelerates uniformly to cover a distance of 6 meters. We are also given the velocity of the body after it has covered the displacement, which is 6 m/s. We need to find the uniform acceleration of the body.
Let's use the equations of motion to solve this problem.
Using the first equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Since the body begins at rest, the initial velocity (u) is 0 m/s.
Substituting the given values:
6 m/s = 0 m/s + a * t
We can see that the time is not given in this problem. However, we know that the body covers a distance of 6 meters during this time.
Using the third equation of motion:
s = ut + (1/2)at^2
where s is the displacement.
Substituting the given values:
6 m = 0 * t + (1/2) * a * t^2
Simplifying the equation:
6 = (1/2) * a * t^2
Dividing both sides of the equation by (1/2) * t^2:
12/t^2 = a
Now, we can substitute this value of a in the first equation of motion:
6 m/s = 0 m/s + (12/t^2) * t
Simplifying the equation:
6 = 12/t
Cross-multiplying:
6t = 12
Dividing both sides of the equation by 6:
t = 2 seconds
Now, we can substitute the value of t in the equation for acceleration:
a = 12/(2^2)
a = 12/4
a = 3 m/s^2
Therefore, the uniform acceleration of the body is 3 m/s^2, which corresponds to option 'C'.
Let's use the equations of motion to solve this problem.
Using the first equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Since the body begins at rest, the initial velocity (u) is 0 m/s.
Substituting the given values:
6 m/s = 0 m/s + a * t
We can see that the time is not given in this problem. However, we know that the body covers a distance of 6 meters during this time.
Using the third equation of motion:
s = ut + (1/2)at^2
where s is the displacement.
Substituting the given values:
6 m = 0 * t + (1/2) * a * t^2
Simplifying the equation:
6 = (1/2) * a * t^2
Dividing both sides of the equation by (1/2) * t^2:
12/t^2 = a
Now, we can substitute this value of a in the first equation of motion:
6 m/s = 0 m/s + (12/t^2) * t
Simplifying the equation:
6 = 12/t
Cross-multiplying:
6t = 12
Dividing both sides of the equation by 6:
t = 2 seconds
Now, we can substitute the value of t in the equation for acceleration:
a = 12/(2^2)
a = 12/4
a = 3 m/s^2
Therefore, the uniform acceleration of the body is 3 m/s^2, which corresponds to option 'C'.
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A body begins at rest and accelerates uniformly to cover a distance of 6 metres. If its velocity after the displacement is 6 m/s, then its uniform acceleration a isa)6 m/s2b)2 m/s2c)3 m/s2d)4 m/s2Correct answer is option 'C'. Can you explain this answer?
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