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The velocity of a particle at an instant is 10 ms-1 After 3 s its velocity will becomes 16 ms-1. The velocity at 2 s, before the given instant will be
- a)6 ms-1
- b)4 ms-1
- c)2 ms-1
- d)1 ms-1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The velocity of a particle at an instant is 10 ms-1 After 3 s its velo...
Here, u = 10ms−1, t = 3s, v = 16ms−1
Now velocity at 2 s, before the given instant
10 = u + 2 x 2
∴ u = 6 m s−1 (since v = u + at)
10 = u + 2 x 2
∴ u = 6 m s−1 (since v = u + at)
Most Upvoted Answer
The velocity of a particle at an instant is 10 ms-1 After 3 s its velo...
Velocity is a vector quantity that describes the rate at which an object changes its position. It has both magnitude and direction. In this question, we are given that the velocity of a particle at an instant is 10 m/s, and after 3 seconds, its velocity becomes 16 m/s. We need to find the velocity at 2 seconds, before the given instant.
Let's break down the problem into two parts:
1. Finding the acceleration:
Acceleration is the rate at which velocity changes with time. It is given by the formula:
acceleration = (change in velocity) / (change in time)
Here, the change in velocity is (16 m/s - 10 m/s) = 6 m/s, and the change in time is (3 s - 0 s) = 3 s.
So, the acceleration is: acceleration = (6 m/s) / (3 s) = 2 m/s^2.
2. Finding the velocity at 2 seconds:
We can use the equation of motion to find the velocity at a given time:
final velocity = initial velocity + (acceleration × time)
Here, the final velocity is 16 m/s, the initial velocity is 10 m/s, and the time is 3 s.
So, we have: 16 m/s = 10 m/s + (2 m/s^2 × 3 s)
Simplifying this equation, we get: 16 m/s = 10 m/s + 6 m/s = 16 m/s
This equation is true, so our calculations are correct.
Now, we need to find the velocity at 2 seconds, before the given instant. We can use the same equation of motion with the time as 2 seconds:
final velocity = initial velocity + (acceleration × time)
We already know the final velocity is 10 m/s, the acceleration is 2 m/s^2, and the time is 2 s.
So, we have: 10 m/s = initial velocity + (2 m/s^2 × 2 s)
Simplifying this equation, we get: 10 m/s = initial velocity + 4 m/s
Subtracting 4 m/s from both sides, we get: initial velocity = 10 m/s - 4 m/s = 6 m/s
Therefore, the velocity at 2 seconds, before the given instant, is 6 m/s.
Let's break down the problem into two parts:
1. Finding the acceleration:
Acceleration is the rate at which velocity changes with time. It is given by the formula:
acceleration = (change in velocity) / (change in time)
Here, the change in velocity is (16 m/s - 10 m/s) = 6 m/s, and the change in time is (3 s - 0 s) = 3 s.
So, the acceleration is: acceleration = (6 m/s) / (3 s) = 2 m/s^2.
2. Finding the velocity at 2 seconds:
We can use the equation of motion to find the velocity at a given time:
final velocity = initial velocity + (acceleration × time)
Here, the final velocity is 16 m/s, the initial velocity is 10 m/s, and the time is 3 s.
So, we have: 16 m/s = 10 m/s + (2 m/s^2 × 3 s)
Simplifying this equation, we get: 16 m/s = 10 m/s + 6 m/s = 16 m/s
This equation is true, so our calculations are correct.
Now, we need to find the velocity at 2 seconds, before the given instant. We can use the same equation of motion with the time as 2 seconds:
final velocity = initial velocity + (acceleration × time)
We already know the final velocity is 10 m/s, the acceleration is 2 m/s^2, and the time is 2 s.
So, we have: 10 m/s = initial velocity + (2 m/s^2 × 2 s)
Simplifying this equation, we get: 10 m/s = initial velocity + 4 m/s
Subtracting 4 m/s from both sides, we get: initial velocity = 10 m/s - 4 m/s = 6 m/s
Therefore, the velocity at 2 seconds, before the given instant, is 6 m/s.
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The velocity of a particle at an instant is 10 ms-1 After 3 s its velocity will becomes 16 ms-1. The velocity at 2 s, before the given instant will bea)6 ms-1b)4 ms-1c)2 ms-1d)1 ms-1Correct answer is option 'A'. Can you explain this answer?
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