Question
\begin{tabular}{l} Anthony is driving to work at a rate of \( 22 \mathrm{~m} / \mathrm{s} \). He glances at the clock in his car and realizes that he is going \\ o be late. Anthony accelerates at a rate of \( 2.8 \mathrm{~m} / \mathrm{s}^{2} \). What will his velocity be after 6 seconds? \\ Equation: \\ \hline\end{tabular}
Ask by Alexander Peterson. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
After 6 seconds, Anthony's velocity will be 38.8 m/s.
Solution
To determine Anthony's velocity after 6 seconds of acceleration, we'll use the following kinematic equation:
\[
v = u + a t
\]
**Where:**
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time
**Given:**
- Initial velocity, \( u = 22 \, \mathrm{m/s} \)
- Acceleration, \( a = 2.8 \, \mathrm{m/s}^2 \)
- Time, \( t = 6 \, \mathrm{seconds} \)
**Plugging in the values:**
\[
v = 22 \, \mathrm{m/s} + (2.8 \, \mathrm{m/s}^2 \times 6 \, \mathrm{seconds})
\]
\[
v = 22 \, \mathrm{m/s} + 16.8 \, \mathrm{m/s}
\]
\[
v = 38.8 \, \mathrm{m/s}
\]
**Answer:**
After 6 seconds, Anthony's velocity will be **38.8 m/s**.
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Simplify this solution Extra Insights
To find Anthony's velocity after 6 seconds, we can use the equation of motion for uniformly accelerated motion: \[ v = u + at \] where: - \( v \) is the final velocity, - \( u \) is the initial velocity (22 m/s), - \( a \) is the acceleration (2.8 m/s²), - \( t \) is the time (6 seconds). Plugging in the values: \[ v = 22 \, \text{m/s} + (2.8 \, \text{m/s}^2 \times 6 \, \text{s}) \] Calculating the acceleration contribution: \[ 2.8 \, \text{m/s}^2 \times 6 \, \text{s} = 16.8 \, \text{m/s} \] Now add this to the initial velocity: \[ v = 22 \, \text{m/s} + 16.8 \, \text{m/s} = 38.8 \, \text{m/s} \] So, Anthony's velocity after 6 seconds will be **38.8 m/s**.
