The velocity of a particle moving with constant acceleration at an instant `t_(0)` is `10m//s` After 5 seconds of that instant the velocity of the particle is 20m/s. The velocity at 3 second before `t_(0)` is:-

Options

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

Answer

To solve the problem step by step, we will use the equations of motion under constant acceleration.

### Step 1: Identify the known values
- Velocity at time \( t_0 \) (initial velocity, \( u \)) = 10 m/s
- Velocity at \( t_0 + 5 \) seconds (final velocity, \( v \)) = 20 m/s
- Time interval = 5 seconds

### Step 2: Use the equation of motion to find acceleration
We can use the equation of motion:
\[ v = u + at \]
Substituting the known values:
\[ 20 = 10 + a \cdot 5 \]
Now, solve for \( a \):
\[ 20 - 10 = 5a \\ 10 = 5a \\ a = \frac{10}{5} = 2 \, \text{m/s}^2 \]

### Step 3: Find the velocity at \( t_0 - 3 \) seconds
Now we need to find the velocity at \( t_0 - 3 \) seconds. We will use the same equation of motion:
\[ v = u + at \]
Here, \( u \) is still 10 m/s, \( a \) is 2 m/s², and the time \( t \) is -3 seconds (since we are looking back in time):
\[ v = 10 + 2 \cdot (-3) \]
Calculating this:
\[ v = 10 - 6 = 4 \, \text{m/s} \]

### Step 4: Conclusion
The velocity of the particle at 3 seconds before \( t_0 \) is **4 m/s**.

---