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Answer :
To solve the problem, follow these steps:
1. Convert the mass from grams to kilograms because the standard unit for mass in the SI system is kilograms. Given that there are [tex]$1000$[/tex] grams in [tex]$1$[/tex] kilogram, we have
[tex]$$
\text{mass in kg} = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}.
$$[/tex]
2. Apply Newton's second law, which is given by
[tex]$$
F = m \cdot a,
$$[/tex]
where [tex]$F$[/tex] is the force in Newtons, [tex]$m$[/tex] is the mass in kilograms, and [tex]$a$[/tex] is the acceleration in [tex]$\text{m/s}^2$[/tex].
3. Substitute the known values into the formula:
[tex]$$
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2.
$$[/tex]
4. Calculate the force:
[tex]$$
F = 3.5 \text{ N}.
$$[/tex]
Therefore, the force needed to accelerate the ball is [tex]$\boxed{3.5 \text{ N}}$[/tex].
1. Convert the mass from grams to kilograms because the standard unit for mass in the SI system is kilograms. Given that there are [tex]$1000$[/tex] grams in [tex]$1$[/tex] kilogram, we have
[tex]$$
\text{mass in kg} = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}.
$$[/tex]
2. Apply Newton's second law, which is given by
[tex]$$
F = m \cdot a,
$$[/tex]
where [tex]$F$[/tex] is the force in Newtons, [tex]$m$[/tex] is the mass in kilograms, and [tex]$a$[/tex] is the acceleration in [tex]$\text{m/s}^2$[/tex].
3. Substitute the known values into the formula:
[tex]$$
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2.
$$[/tex]
4. Calculate the force:
[tex]$$
F = 3.5 \text{ N}.
$$[/tex]
Therefore, the force needed to accelerate the ball is [tex]$\boxed{3.5 \text{ N}}$[/tex].
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