A car is stopped at a red traffic light. When the light turns to green, the car has a constant acceleration and crosses the 9.10 m intersection in 2.47 s. What is the magnitude of the car's acceleration ?

Options

A. 13 m, 37 m
B. 16 m, 41 m
C. 17 m, 44 m
D. 14 m, 28 m

Answer

To find the magnitude of the car's acceleration, we can use the second equation of motion, which relates displacement, initial velocity, time, and acceleration. The equation is:

\[ s = ut + \frac{1}{2} a t^2 \]

### Step-by-Step Solution:

1. **Identify the known values**:
- Displacement \( s = 9.10 \, \text{m} \)
- Initial velocity \( u = 0 \, \text{m/s} \) (the car starts from rest)
- Time \( t = 2.47 \, \text{s} \)

2. **Substitute the known values into the equation**:
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 9.10 = \frac{1}{2} a (2.47)^2 \]

3. **Calculate \( (2.47)^2 \)**:
\[ (2.47)^2 = 6.1009 \]
So the equation becomes:
\[ 9.10 = \frac{1}{2} a \cdot 6.1009 \]

4. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \cdot 9.10 = a \cdot 6.1009 \]
\[ 18.20 = a \cdot 6.1009 \]

5. **Solve for \( a \)**:
\[ a = \frac{18.20}{6.1009} \]
\[ a \approx 2.98 \, \text{m/s}^2 \]

### Final Answer:
The magnitude of the car's acceleration is approximately \( 2.98 \, \text{m/s}^2 \).

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