The velocity of a particle at an instant is 10m/s. After 5sec, the velocity of the particle is 20m/s. Find the velocity at 3 seconds before from the instant when velocity of a particle is 10m/s.

Options

A. 8m/s
B. 4m/s
C. 6m/s
D. 7m/s

Explanation

To solve the problem step by step, we need to find the velocity of the particle 3 seconds before the instant when its velocity is 10 m/s.

### Step 1: Understand the given information
- Initial velocity (v₀) at time t = 0 seconds: 10 m/s
- Final velocity (v) after 5 seconds: 20 m/s
- Time interval (t) = 5 seconds

### Step 2: Calculate the acceleration
Using the equation of motion:
\[ v = u + at \]
Where:
- \( v \) = final velocity = 20 m/s
- \( u \) = initial velocity = 10 m/s
- \( a \) = acceleration (unknown)
- \( t \) = time interval = 5 seconds

Substituting the known values:
\[ 20 = 10 + a \cdot 5 \]

Rearranging the equation to solve for \( a \):
\[ 20 - 10 = 5a \]
\[ 10 = 5a \]
\[ a = \frac{10}{5} = 2 \text{ m/s}^2 \]

### Step 3: Determine the velocity 3 seconds before the instant when the velocity is 10 m/s
Now we need to find the velocity 3 seconds before the time when the velocity is 10 m/s. This means we need to find the initial velocity (u) at \( t = -3 \) seconds.

Using the same equation of motion:
\[ v = u + at \]
Where:
- \( v \) = final velocity = 10 m/s (at t = 0 seconds)
- \( u \) = initial velocity (unknown, at t = -3 seconds)
- \( a \) = 2 m/s² (calculated from Step 2)
- \( t \) = 3 seconds

Substituting the known values:
\[ 10 = u + 2 \cdot 3 \]

Rearranging the equation to solve for \( u \):
\[ 10 = u + 6 \]
\[ u = 10 - 6 \]
\[ u = 4 \text{ m/s} \]

### Conclusion
The velocity of the particle 3 seconds before the instant when its velocity is 10 m/s is **4 m/s**.