To answer this question, we need to follow a step-by-step approach to determine the force acting on the boulder.
### Step 1: Understand the given information
- Mass of the boulder ([tex]\( m \)[/tex]): 200 kg
- Initial speed ([tex]\( u \)[/tex]): 0 m/s (since it was initially at rest)
- Final speed ([tex]\( v \)[/tex]): 3.5 m/s
- Time taken ([tex]\( t \)[/tex]): 10 seconds
### Step 2: Calculate the acceleration
Acceleration ([tex]\( a \)[/tex]) can be calculated using the formula from kinematics:
[tex]\[ a = \frac{v - u}{t} \][/tex]
where:
- [tex]\( v \)[/tex] is the final speed,
- [tex]\( u \)[/tex] is the initial speed,
- [tex]\( t \)[/tex] is the time taken.
Plugging in the values:
[tex]\[ a = \frac{3.5 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = \frac{3.5 \, \text{m/s}}{10 \, \text{s}} = 0.35 \, \text{m/s}^2 \][/tex]
So, the acceleration [tex]\( a \)[/tex] is [tex]\( 0.35 \, \text{m/s}^2 \)[/tex].
### Step 3: Calculate the force
To find the force acting on the boulder, we use Newton's second law of motion, which states:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
Plugging in the values:
[tex]\[ F = 200 \, \text{kg} \times 0.35 \, \text{m/s}^2 = 70 \, \text{N} \][/tex]
### Conclusion
The force acting on the boulder is [tex]\( 70 \, \text{N} \)[/tex].
