Certainly! Let's complete the given table based on the problem details.
1. At [tex]\( t = 2 \)[/tex] seconds:
- Displacement [tex]\( s \)[/tex]:
- We can calculate displacement using the equation:
[tex]\[
s = \frac{1}{2} \cdot a \cdot t^2
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 2 \, \text{s} \)[/tex], we get:
[tex]\[
s = \frac{1}{2} \cdot 2 \cdot (2^2) = 4 \, \text{m}
\][/tex]
- Velocity [tex]\( v \)[/tex]:
- The velocity can be found using the equation:
[tex]\[
v = a \cdot t
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 2 \, \text{s} \)[/tex], we get:
[tex]\[
v = 2 \cdot 2 = 4 \, \text{m/s}
\][/tex]
2. When the final velocity is [tex]\( 10 \, \text{m/s} \)[/tex]:
- Time [tex]\( t \)[/tex]:
- To find the time taken to reach this velocity:
[tex]\[
t = \frac{v}{a}
\][/tex]
Given [tex]\( v = 10 \, \text{m/s} \)[/tex] and [tex]\( a = 2 \, \text{m/s}^2 \)[/tex], we get:
[tex]\[
t = \frac{10}{2} = 5 \, \text{s}
\][/tex]
- Displacement [tex]\( s \)[/tex]:
- Using the displacement equation:
[tex]\[
s = \frac{1}{2} \cdot a \cdot t^2
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 5 \, \text{s} \)[/tex], we get:
[tex]\[
s = \frac{1}{2} \cdot 2 \cdot (5^2) = 25 \, \text{m}
\][/tex]
3. When the displacement is [tex]\( 25 \, \text{m} \)[/tex]:
- Time [tex]\( t \)[/tex]:
- Using the displacement equation, we can solve for time [tex]\( t \)[/tex]:
[tex]\[
25 = \frac{1}{2} \cdot 2 \cdot t^2
\][/tex]
Solving for [tex]\( t \)[/tex]:
[tex]\[
25 = t^2 \implies t = \sqrt{25} = 5 \, \text{s}
\][/tex]
- Velocity [tex]\( v \)[/tex]:
- Using the velocity equation:
[tex]\[
v = a \cdot t
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 5 \, \text{s} \)[/tex], we get:
[tex]\[
v = 2 \cdot 5 = 10 \, \text{m/s}
\][/tex]
4. At [tex]\( t = 10 \, \text{minutes} \)[/tex] or [tex]\( 600 \, \text{seconds} \)[/tex]:
- Displacement [tex]\( s \)[/tex]:
- Using the displacement equation:
[tex]\[
s = \frac{1}{2} \cdot a \cdot t^2
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 600 \, \text{s} \)[/tex], we get:
[tex]\[
s = \frac{1}{2} \cdot 2 \cdot (600^2) = 360000 \, \text{m}
\][/tex]
- Velocity [tex]\( v \)[/tex]:
- Using the velocity equation:
[tex]\[
v = a \cdot t
\][/tex]
Given [tex]\( a = 2 \, \text{m/s}^2 \)[/tex] and [tex]\( t = 600 \, \text{s} \)[/tex], we get:
[tex]\[
v = 2 \cdot 600 = 1200 \, \text{m/s}
\][/tex]
Here is the completed table:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Time} & \text{Displacement} & \text{Velocity} \\
\hline
2 \, \text{s} & 4 \, \text{m} & 4 \, \text{m/s} \\
\hline
5 \, \text{s} & 25 \, \text{m} & 10 \, \text{m/s} \\
\hline
5 \, \text{s} & 25 \, \text{m} & 10 \, \text{m/s} \\
\hline
10 \, \text{min} & 360000 \, \text{m} & 1200 \, \text{m/s} \\
\hline
\end{array}
\][/tex]
