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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 find the force needed to accelerate the ball, we use the formula:

[tex]\[ F = ma \][/tex]

where
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( a \)[/tex] is the acceleration.

Step 1: Convert the mass to kilograms.
The mass of the ball is given as 140 grams, which needs to be converted to kilograms since the standard unit for mass in physics is kilograms. There are 1000 grams in a kilogram, so:

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

Step 2: Use the acceleration.
The acceleration is given as [tex]\( 25 \, \text{m/s}^2 \)[/tex].

Step 3: Calculate the force.
Now we substitute the values into the formula:

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

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

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

Therefore, the force needed to accelerate the ball at [tex]\( 25 \, \text{m/s}^2 \)[/tex] is [tex]\( 3.5 \, \text{N} \)[/tex].

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