meganknott121
Answered

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A rock is rolling down a hill. At position 1, its velocity is 2.0 m/s. Twelve seconds later, as it passes position 2, its velocity is 44.0 m/s. What is the acceleration of the rock?

A. 3.5 m/s²
B. 3.7 m/s²
C. 3.8 m/s²
D. 42.0 m/s²

Sagot :

GinnyAnswer
To determine the acceleration of the rock, we use the following basic kinematic formula:

[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]

Where:
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( v_f \)[/tex] is the final velocity,
- [tex]\( v_i \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time.

Given:
- The initial velocity ([tex]\( v_i \)[/tex]) is [tex]\( 2.0 \, \text{m/s} \)[/tex],
- The final velocity ([tex]\( v_f \)[/tex]) is [tex]\( 44.0 \, \text{m/s} \)[/tex],
- The time ([tex]\( t \)[/tex]) is [tex]\( 12 \, \text{seconds} \)[/tex].

Now, let's substitute these values into the formula to find the acceleration:

[tex]\[ a = \frac{{44.0 \, \text{m/s} - 2.0 \, \text{m/s}}}{12 \, \text{seconds}} \][/tex]

[tex]\[ a = \frac{42.0 \, \text{m/s}}{12 \, \text{seconds}} \][/tex]

[tex]\[ a = 3.5 \, \text{m/s}^2 \][/tex]

Therefore, the acceleration of the rock is [tex]\( 3.5 \, \text{m/s}^2 \)[/tex].

The correct answer is [tex]\( 3.5 \, \text{m/s}^2 \)[/tex].
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