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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, you can use the formula:

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

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

### Step-by-Step Solution:

1. Convert Mass to Kilograms:
- The mass of the ball is given as 140 grams.
- To use the formula, convert this mass to kilograms since the standard unit of mass in the formula is kilograms.
- There are 1000 grams in 1 kilogram, so:
[tex]\[
m = \frac{140 \, \text{g}}{1000} = 0.14 \, \text{kg}
\][/tex]

2. Use the Formula [tex]\( F = ma \)[/tex]:
- Now that the mass is in kilograms, you can use the formula to find the force.
- The acceleration is given as 25 m/s².
- Substitute the values into the formula:
[tex]\[
F = 0.14 \, \text{kg} \times 25 \, \text{m/s}^2
\][/tex]

3. Calculate the Force:
- Multiply the mass by the acceleration:
[tex]\[
F = 3.5 \, \text{N}
\][/tex]

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

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