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A ball has a mass of 140 g. What is the force needed to accelerate the ball at [tex]$25 \, \text{m/s}^2$[/tex]?

(Formula: [tex]$F = ma$[/tex])

A. 3.5 N
B. 115 N
C. 165 N
D. 4.5 N

Answer :

To solve this problem, we start by converting the mass from grams to kilograms. Since there are 1000 grams in a kilogram, the mass in kilograms is

[tex]$$
m = \frac{140 \text{ g}}{1000} = 0.14 \text{ kg}.
$$[/tex]

Newton's second law states that the force required is given by

[tex]$$
F = m \times a,
$$[/tex]

where [tex]\( m \)[/tex] is the mass and [tex]\( a \)[/tex] is the acceleration. Given that the acceleration is

[tex]$$
a = 25 \text{ m/s}^2,
$$[/tex]

we substitute the values into the formula:

[tex]$$
F = 0.14 \text{ kg} \times 25 \text{ m/s}^2.
$$[/tex]

Multiplying these values, we have

[tex]$$
F = 3.5 \text{ N}.
$$[/tex]

Thus, the force needed to accelerate the ball is [tex]\(\boxed{3.5 \text{ N}}\)[/tex].

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