Question

choose the equation that helps solve the following problem most easily... a car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. determine the acceleration of the car. (hint: v₀ = v₁)
d = v₀t+\frac{1}{2}at² (hint: v₀ = v₁)
d = \frac{v₀ + v_f}{2}·t (hint: v₀ = v₁)
v_f² = v₀²+2ad (hint: v₀ = v₁)
v_f = v₀+at (hint: v₀ = v₁)

Explanation:

Step1: Identify given values

The car starts from rest, so $v_0 = 0$. The time $t = 5.21$ s and the distance $d=110$ m. We want to find the acceleration $a$.

Step2: Analyze each equation

• For $d = v_0t+\frac{1}{2}at^{2}$, substituting $v_0 = 0$ gives $d=\frac{1}{2}at^{2}$, which can be easily solved for $a$.
• For $d=\frac{v_0 + v_f}{2}\cdot t$, we don't know $v_f$ and it requires extra steps to find $a$.
• For $v_f^{2}=v_0^{2}+2ad$, we don't know $v_f$ and it will lead to more complex calculations.
• For $v_f=v_0 + at$, we don't know $v_f$ and it is not straightforward to find $a$.

Answer:

$d = v_0t+\frac{1}{2}at^{2}$