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Answer :
To solve for the force needed to accelerate the ball, we start with the formula
[tex]$$F = m \cdot a,$$[/tex]
where
- [tex]$F$[/tex] is the force,
- [tex]$m$[/tex] is the mass, and
- [tex]$a$[/tex] is the acceleration.
1. The mass of the ball is given as 140 g. Since the standard unit of mass for this formula is kilograms (kg), we first convert the mass from grams to kilograms. Knowing that 1000 g = 1 kg, we have
[tex]$$ m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}. $$[/tex]
2. The acceleration is given as [tex]$25 \text{ m/s}^2$[/tex].
3. Now, substitute the values for mass and acceleration into the formula:
[tex]$$ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2. $$[/tex]
4. Multiplying these together gives:
[tex]$$ F = 3.5 \text{ N}. $$[/tex]
Thus, the force needed to accelerate the ball at [tex]$25 \text{ m/s}^2$[/tex] is
[tex]$$ \boxed{3.5 \text{ N}}. $$[/tex]
[tex]$$F = m \cdot a,$$[/tex]
where
- [tex]$F$[/tex] is the force,
- [tex]$m$[/tex] is the mass, and
- [tex]$a$[/tex] is the acceleration.
1. The mass of the ball is given as 140 g. Since the standard unit of mass for this formula is kilograms (kg), we first convert the mass from grams to kilograms. Knowing that 1000 g = 1 kg, we have
[tex]$$ m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}. $$[/tex]
2. The acceleration is given as [tex]$25 \text{ m/s}^2$[/tex].
3. Now, substitute the values for mass and acceleration into the formula:
[tex]$$ F = 0.14 \text{ kg} \times 25 \text{ m/s}^2. $$[/tex]
4. Multiplying these together gives:
[tex]$$ F = 3.5 \text{ N}. $$[/tex]
Thus, the force needed to accelerate the ball at [tex]$25 \text{ m/s}^2$[/tex] is
[tex]$$ \boxed{3.5 \text{ N}}. $$[/tex]
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