Question

a beetle accidentally rolls onto its back and begins to slide down a leaf which is at an angle and acts like a ramp. the beetle starts from rest, and experiences a constant acceleration down the leaf
amp.\ the beetle has a displacement of 0.2 meters in 3 seconds. what must be the acceleration of the beetle down the ramp?

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for an object starting from rest ($v_0 = 0$) is $x=v_0t+\frac{1}{2}at^{2}$. 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 $x=\frac{1}{2}at^{2}$ for $a$. Multiply both sides by 2 and divide by $t^{2}$ to get $a=\frac{2x}{t^{2}}$.

Step3: Substitute the given values

We are given that $x = 0.2$ m and $t = 3$ s. Substituting these values into the formula $a=\frac{2x}{t^{2}}$, we have $a=\frac{2\times0.2}{3^{2}}=\frac{0.4}{9}\approx0.044$ m/s².

Answer:

$a\approx0.044$ m/s²