Question

which equation can be used to solve for acceleration?
○ ( t = \frac{delta v}{a} )
○ ( v_f = at - v_i )
○ ( a = \frac{d}{t} )
○ ( delta v = \frac{a}{t} )

Explanation:

Step1: Recall the definition of acceleration

Acceleration \( a \) is defined as the change in velocity \( \Delta v \) over time \( t \), so the formula is \( a=\frac{\Delta v}{t} \), which can be rearranged. Let's analyze each option:

Step2: Analyze Option 1 (\( t = \frac{\Delta v}{a} \))

Starting from the acceleration formula \( a=\frac{\Delta v}{t} \), we can multiply both sides by \( t \) to get \( at=\Delta v \), then divide both sides by \( a \) (assuming \( a
eq0 \)) to get \( t = \frac{\Delta v}{a} \). This equation can be rearranged to solve for \( a \) (by cross - multiplying: \( a=\frac{\Delta v}{t} \)), so this equation can be used to solve for acceleration.

Step3: Analyze Option 2 (\( v_f=at - v_i \))

The correct kinematic equation for final velocity is \( v_f=v_i + at \). Rearranging \( v_f=at - v_i \) would give \( at=v_f + v_i \), and \( a=\frac{v_f + v_i}{t} \), which is not the correct formula for acceleration (acceleration is change in velocity over time, \( \Delta v=v_f - v_i \), so \( a = \frac{v_f - v_i}{t} \)), so this equation is incorrect.

Step4: Analyze Option 3 (\( a=\frac{d}{t} \))

The formula \( \frac{d}{t} \) gives the average speed (when \( d \) is distance), not acceleration. Acceleration is related to change in velocity, not distance over time, so this is incorrect.

Step5: Analyze Option 4 (\( \Delta v=\frac{a}{t} \))

From the correct acceleration formula \( a=\frac{\Delta v}{t} \), we can multiply both sides by \( t \) to get \( \Delta v = at \), not \( \Delta v=\frac{a}{t} \), so this equation is incorrect.

Answer:

The equation that can be used to solve for acceleration is \( \boldsymbol{t=\frac{\Delta v}{a}} \) (since it can be rearranged to \( a = \frac{\Delta v}{t} \)).