Given:
- Constant acceleration, $ a = 1 \, \text{m/s}^2 $
- Time, $ t = 10 \, \text{s} $
- Final velocity, $ v = 5 \, \text{m/s} $
- Initial and final velocities are in opposite directions.

Step-by-step solution:

1. **Determine the initial velocity ($ u $):**

Since the initial and final velocities are in opposite directions, the final velocity will be negative when considering the initial direction as positive.

Using the equation of motion:
$$
v = u + at
$$
Substituting the given values:
$$
5 = u + (1 \times 10)
$$
$$
5 = u + 10
$$
Solving for $ u $:
$$
u = 5 - 10
$$
$$
u = -5 \, \text{m/s}
$$

2. **Calculate the distance covered ($ s $):**

Using the equation of motion:
$$
s = ut + \frac{1}{2}at^2
$$
Substituting the known values:
$$
s = (-5 \times 10) + \frac{1}{2} \times 1 \times (10)^2
$$
$$
s = -50 + \frac{1}{2} \times 1 \times 100
$$
$$
s = -50 + 50
$$
$$
s = 0 \, \text{m}
$$

Therefore, the distance covered by the particle in this duration is $ 0 \, \text{m} $.

Question

Given:
- Constant acceleration, $ a = 1 \, \text{m/s}^2 $
- Time, $ t = 10 \, \text{s} $
- Final velocity, $ v = 5 \, \text{m/s} $
- Initial and final velocities are in opposite directions.

Step-by-step solution:

1. **Determine the initial velocity ($ u $):**

Since the initial and final velocities are in opposite directions, the final velocity will be negative when considering the initial direction as positive.

Using the equation of motion:
   $$
   v = u + at
   $$
   Substituting the given values:
   $$
   5 = u + (1 \times 10)
   $$
   $$
   5 = u + 10
   $$
   Solving for $ u $:
   $$
   u = 5 - 10
   $$
   $$
   u = -5 \, \text{m/s}
   $$

2. **Calculate the distance covered ($ s $):**

Using the equation of motion:
   $$
   s = ut + \frac{1}{2}at^2
   $$
   Substituting the known values:
   $$
   s = (-5 \times 10) + \frac{1}{2} \times 1 \times (10)^2
   $$
   $$
   s = -50 + \frac{1}{2} \times 1 \times 100
   $$
   $$
   s = -50 + 50
   $$
   $$
   s = 0 \, \text{m}
   $$

Therefore, the distance covered by the particle in this duration is $ 0 \, \text{m} $.

Knowee AI · Accepted Answer

Given:
- Constant acceleration, $ a = 1 \, \text{m/s}^2 $
- Time, $ t = 10 \, \text{s} $
- Final velocity, $ v = 5 \, \text{m/s} $
- Initial and final velocities are in opposite directions.

Step-by-step solution:

1. **Determine the initial velocity ($ u $):**

Since the initial and final velocities are in opposite directions, the final velocity will be negative when considering the initial direction as positive.

Using the equation of motion:
   $$
   v = u + at
   $$
   Substituting the given values:
   $$
   5 = u + (1 \times 10)
   $$
   $$
   5 = u + 10
   $$
   Solving for $ u $:
   $$
   u = 5 - 10
   $$
   $$
   u = -5 \, \text{m/s}
   $$

2. **Calculate the distance covered ($ s $):**

Using the equation of motion:
   $$
   s = ut + \frac{1}{2}at^2
   $$
   Substituting the known values:
   $$
   s = (-5 \times 10) + \frac{1}{2} \times 1 \times (10)^2
   $$
   $$
   s = -50 + \frac{1}{2} \times 1 \times 100
   $$
   $$
   s = -50 + 50
   $$
   $$
   s = 0 \, \text{m}
   $$

Therefore, the distance covered by the particle in this duration is $ 0 \, \text{m} $.

A particle moves rectilinearly with a constant acceleration 1 m/s2. Its speed after 10 seconds is 5 m/s. The distance covered by the particle in this duration is (Initial & final velocities are in opposite direction)

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