Question

question 16
a car is stopped at a red traffic light. when the light turns to green, the car has a constant acceleration and crosses the 9.10 - m intersection in 2.86 s. what is the magnitude of the cars acceleration?
7.36 m/s²
9.80 m/s²
2.98 m/s²
1.77 m/s²
2.23 m/s²

Explanation:

Step1: Identify the kinematic - equation

The car starts from rest ($v_0 = 0$), and the kinematic equation $x=v_0t+\frac{1}{2}at^{2}$ is used. Since $v_0 = 0$, the equation simplifies to $x=\frac{1}{2}at^{2}$.

Step2: Solve for acceleration $a$

We can re - arrange the equation $x=\frac{1}{2}at^{2}$ to solve for $a$. We get $a=\frac{2x}{t^{2}}$.

Step3: Substitute the given values

Given $x = 9.10$ m and $t = 2.86$ s. Substitute these values into the formula: $a=\frac{2\times9.10}{(2.86)^{2}}$.
$a=\frac{18.2}{8.1796}\approx2.23$ m/s²

Answer:

$2.23$ m/s²