Question

1. an object is sliding from rest down a frictionless inclined plane. the object slides 1.0 m during the first second. what distance will the object slide during the next second? a. 1.0 m b. 2.0 m c. 3.0 m d. 4.9 m

Explanation:

Step1: Determine the acceleration

The object starts from rest ($u = 0$), and the displacement - time formula is $s=ut+\frac{1}{2}at^{2}$. Given $s = 1.0m$ and $t = 1s$ and $u = 0$, substituting into the formula $s=ut+\frac{1}{2}at^{2}$ gives $1=0\times1+\frac{1}{2}a\times(1)^{2}$. Solving for $a$:
\[

$$\begin{align*} 1&=\frac{1}{2}a\times1\\ a& = 2m/s^{2} \end{align*}$$

\]

Step2: Calculate the displacement in the first 2 seconds

Using the formula $s=ut+\frac{1}{2}at^{2}$ again, with $u = 0$, $a = 2m/s^{2}$ and $t = 2s$, we have $s_{2}=0\times2+\frac{1}{2}\times2\times(2)^{2}=4m$.

Step3: Calculate the displacement in the second - second

The displacement in the second - second ($s_{1 - 2}$) is the displacement in the first 2 seconds minus the displacement in the first second. The displacement in the first second $s_{1}=1m$. So $s_{1 - 2}=s_{2}-s_{1}=4 - 1=3m$.

Answer:

C. 3.0 m