To find the force required to accelerate an object, you can use Newton's second law of motion, which states:
\[ F = m \cdot a \]
where:
- \( F \) is the force,
- \( m \) is the mass of the object, and
- \( a \) is the acceleration.
For the toy train:
- \( m = 6.8 , \text{kg} \)
- \( a = 13 , \text{m/s}^2 \)
Now, substitute the values into the formula:
\[ F = 6.8 , \text{kg} \cdot 13 , \text{m/s}^2 \]
Calculating that:
\[ F = 88.4 , \text{N} \]
So, the force required to accelerate the toy train at \( 13 , \text{m/s}^2 \) is 88.4 Newtons.