A car moving in a straight line starts at 𝑥 = 0 x=0 at 𝑡 = 0 t=0. It passes: Point 𝑥 = 29.0 m x=29.0m with speed 11.5 m/s 11.5m/s at 𝑡 = 3.00 s t=3.00s Point 𝑥 = 375 m x=375m with speed 44.0 m/s 44.0m/s at 𝑡 = 20.0 s t=20.0s

 

Car Motion Analysis

A car moving in a straight line starts at \( x = 0 \) at \( t = 0 \). It passes:

• Point \( x = 29.0 \, \text{m} \) with speed \( 11.5 \, \text{m/s} \) at \( t = 3.00 \, \text{s} \)
• Point \( x = 375 \, \text{m} \) with speed \( 44.0 \, \text{m/s} \) at \( t = 20.0 \, \text{s} \)

Part A: Average Velocity

Find the average velocity between \( t = 3.00 \, \text{s} \) and \( t = 20.0 \, \text{s} \).

\[ \text{Average velocity} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1} \]

Given:

• \( x_1 = 29.0 \, \text{m} \) at \( t_1 = 3.00 \, \text{s} \)
• \( x_2 = 375 \, \text{m} \) at \( t_2 = 20.0 \, \text{s} \)

Calculation:

\[ \Delta x = 375 \, \text{m} - 29.0 \, \text{m} = 346 \, \text{m} \]

\[ \Delta t = 20.0 \, \text{s} - 3.00 \, \text{s} = 17.0 \, \text{s} \]

\[ \text{Average velocity} = \frac{346 \, \text{m}}{17.0 \, \text{s}} = 20.4 \, \text{m/s} \]

Final Answer:

\( 20.4 \, \frac{\text{m}}{\text{s}} \)

✔ Correct

Part B: Average Acceleration

Find the average acceleration between \( t = 3.00 \, \text{s} \) and \( t = 20.0 \, \text{s} \).

\[ \text{Average acceleration} = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1} \]

Given:

• \( v_1 = 11.5 \, \text{m/s} \) at \( t_1 = 3.00 \, \text{s} \)
• \( v_2 = 44.0 \, \text{m/s} \) at \( t_2 = 20.0 \, \text{s} \)

Calculation:

\[ \Delta v = 44.0 \, \text{m/s} - 11.5 \, \text{m/s} = 32.5 \, \text{m/s} \]

\[ \Delta t = 20.0 \, \text{s} - 3.00 \, \text{s} = 17.0 \, \text{s} \]

\[ \text{Average acceleration} = \frac{32.5 \, \text{m/s}}{17.0 \, \text{s}} = 1.91 \, \text{m/s}^2 \]

Final Answer:

\( 1.91 \, \frac{\text{m}}{\text{s}^2} \)

✔ Correct