Answer :
To solve the problem, first note that the formula for force is given by
$$
F = m \cdot a,
$$
where:
- $F$ is the force,
- $m$ is the mass,
- $a$ is the acceleration.
**Step 1: Convert the mass to kilograms**
The mass is given as 140 grams. Since there are 1000 grams in 1 kilogram, convert the mass to kilograms:
$$
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}.
$$
**Step 2: Calculate the force**
The acceleration is given as $25 \, \text{m/s}^2$. Substitute the values into the formula:
$$
F = 0.14 \text{ kg} \times 25 \, \text{m/s}^2.
$$
**Step 3: Perform the multiplication**
$$
F = 3.5 \, \text{N}.
$$
Thus, the force needed to accelerate the ball is $\boxed{3.5 \, \text{N}}$.
$$
F = m \cdot a,
$$
where:
- $F$ is the force,
- $m$ is the mass,
- $a$ is the acceleration.
**Step 1: Convert the mass to kilograms**
The mass is given as 140 grams. Since there are 1000 grams in 1 kilogram, convert the mass to kilograms:
$$
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}.
$$
**Step 2: Calculate the force**
The acceleration is given as $25 \, \text{m/s}^2$. Substitute the values into the formula:
$$
F = 0.14 \text{ kg} \times 25 \, \text{m/s}^2.
$$
**Step 3: Perform the multiplication**
$$
F = 3.5 \, \text{N}.
$$
Thus, the force needed to accelerate the ball is $\boxed{3.5 \, \text{N}}$.
