Which equation can be used to solve for acceleration?

Ask by Vaughan Beck. in the United States

Jan 24,2025

Question

Which equation can be used to solve for acceleration? $$ v=\frac{\Delta v}{a} $$ $$ a=\frac{d}{t} $$ $$ \Delta v=\frac{a}{t} $$

UpStudy AI · Accepted Answer

None of the provided equations correctly represent the relationship for solving acceleration. Let's review each option and then provide the correct equation for acceleration.

### Review of Given Equations:

1. **$$ v = \frac{\Delta v}{a} $$**
   - **Analysis:** This equation rearranges to $$ a = \frac{\Delta v}{v} $$, which is not the standard definition of acceleration.
   - **Conclusion:** **Incorrect**

2. **$$ a = \frac{d}{t} $$**
   - **Analysis:** This equation suggests that acceleration is equal to displacement divided by time. However, displacement divided by time actually represents **average velocity** when starting from rest, not acceleration.
   - **Conclusion:** **Incorrect**

3. **$$ \Delta v = \frac{a}{t} $$**
   - **Analysis:** Rearranging gives $$ a = \Delta v \times t $$, which is not the standard relationship. The correct relationship involves division by time, not multiplication.
   - **Conclusion:** **Incorrect**

### Correct Equation for Acceleration:

The standard definition of acceleration ($$ a $$) is the **change in velocity** ($$ \Delta v $$) **divided by the time** ($$ t $$) over which that change occurs. Mathematically, this is expressed as:

$$
a = \frac{\Delta v}{t}
$$

### Example Usage:

If a car increases its velocity by $$ 20 \, \text{m/s} $$ over $$ 5 $$ seconds, the acceleration would be:

$$
a = \frac{20 \, \text{m/s}}{5 \, \text{s}} = 4 \, \text{m/s}^2
$$

### Additional Kinematic Equations Involving Acceleration:

Acceleration appears in various kinematic equations that relate displacement ($$ d $$), initial velocity ($$ v_0 $$), final velocity ($$ v $$), time ($$ t $$), and acceleration ($$ a $$):

1. **Final Velocity:**
   $$
   v = v_0 + a t
   $$

2. **Displacement with Constant Acceleration:**
   $$
   d = v_0 t + \frac{1}{2} a t^2
   $$

3. **Velocity-Squared Relation:**
   $$
   v^2 = v_0^2 + 2 a d
   $$

These equations are fundamental in physics for solving problems involving uniformly accelerated motion.
None of the provided equations correctly represent the relationship for solving acceleration. The correct equation is $$ a = \frac{\Delta v}{t} $$.

Which equation can be used to solve for acceleration?

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