Question

1. starting from rest, an object rolls freely down an incline that is 10 meters long in 2 seconds. the acceleration of the object is approximately a) 5 m/sec b) 5 m/sec² c) 10 m/sec d) 10 m/sec²

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for motion with constant acceleration 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 $x=\frac{1}{2}at^{2}$ to solve for $a$. Multiply both sides by 2 to get $2x = at^{2}$, then $a=\frac{2x}{t^{2}}$.

Step3: Substitute the given values

We are given that $x = 10$ m and $t = 2$ s. Substitute these values into the formula: $a=\frac{2\times10}{2^{2}}=\frac{20}{4}=5$ m/s².

Answer:

B. 5 m/sec²