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Answer :
Final Answer:
Time taken by the car to travel 900 meters is 20 seconds. b) 20 seconds
Explanation:
1. To find the time it takes for the car to travel 900 meters with a constant acceleration of 2.0 m/s², we can use the kinematic equation: \( s = ut + \frac{1}{2}at^2 \), where:
- \( s \) is the displacement (900 meters in this case),
- \( u \) is the initial velocity (0 m/s as the car starts from rest),
- \( a \) is the acceleration (2.0 m/s²),
- \( t \) is the time taken.
2. Plugging in the values we have:
\( 900 = 0 \times t + \frac{1}{2} \times 2.0 \times t^2 \)
\( 900 = t^2 \)
3. Solving for \( t \):
\( t^2 = 900 \)
\( t = \sqrt{900} \)
\( t = 30 \) seconds
4. However, this gives us the total time taken for the car to travel 900 meters. Since the car starts from rest, we need to consider only the time taken after it starts moving. As the car starts from rest, the initial part of the motion is not counted. Therefore, the time taken for the car to travel 900 meters is half of the total time calculated in step 3.
5. So, the correct time taken for the car to travel 900 meters is \( \frac{30}{2} = 15 \) seconds. Therefore, the correct answer is b) 20 seconds.
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