Final answer:
The average acceleration of the drag racer is calculated using kinematic equations. After converting the final velocity to meters per second, the calculation shows an average acceleration of approximately 38.01 m/s^2 over the time period and 52.06 m/s^2 over the distance, but these results do not match the given answer choices, suggesting an error.
Step-by-step explanation:
To find the average acceleration of the drag racer, we can use the following kinematic equation:
\(a = \frac{v_f - v_i}{t}\)
where:
- \(a\) is the average acceleration
- \(v_f\) is the final velocity
- \(v_i\) is the initial velocity (which we can assume as 0 since the dragster starts from rest)
- \(t\) is the time taken to reach the final velocity
First, we convert the final velocity from km/hr to m/s:
\(520 \frac{km}{hr} \times \frac{1000 m}{1 km} \times \frac{1 hr}{3600 s} = 144.44 \frac{m}{s}\)
Now we can calculate the average acceleration:
\(a = \frac{144.44 m/s - 0 m/s}{3.8 s} = 38.01 m/s^2\)
To find the average acceleration over the distance of 400m, we can use another kinematic equation:
\(v_f^2 = v_i^2 + 2a \times d\)
where:
- \(v_f\) is the final velocity (144.44 m/s)
- \(v_i\) is the initial velocity (0 m/s)
- \(a\) is the average acceleration
- \(d\) is the distance traveled (400m)
Solving for acceleration yields:
\(a = \frac{v_f^2 - v_i^2}{2d} = \frac{(144.44 m/s)^2}{2 \times 400 m} \approx 52.06 m/s^2\)
However, none of the provided answer choices (137.89 m/s^2, 145.26 m/s^2, 129.47 m/s^2, 132.63 m/s^2) corresponds to the calculated value. It appears there might be an error in the question or the provided answer choices.