Question

A particle moving in air increases its speed within 30 minutes. Find its acceleration.
1. Its initial velocity is 20 miles per hour and its final velocity is 25 miles per hour.
2. The particle increases its speed by 5 miles per hour.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask.
• D. EACH statement ALONE is sufficient to answer the question asked.
• E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hint:

Recognize that different pieces of information can lead to the same result. Statement (1) gives initial and final velocities, while Statement (2) gives the change in velocity directly. Both allow the calculation of acceleration, making each statement sufficient on its own.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The question asks for the acceleration of a particle. We are given the time interval. We need to determine if the statements provide enough information about the change in velocity to calculate the acceleration.
Step 2: Key Formula or Approach:
Acceleration is the rate of change of velocity. The formula is:
\[ \text{Acceleration} (a) = \frac{\text{Final Velocity} (v) - \text{Initial Velocity} (u)}{\text{Time} (t)} = \frac{\Delta v}{t} \] From the question, we know the time: \( t = 30 \text{ minutes} = 0.5 \text{ hours} \).
To find the acceleration, we need the change in velocity ($v - u$).
Step 3: Detailed Explanation:
Analyze Statement (1): "Its initial velocity is 20 miles per hour and its final velocity is 25 miles per hour."
This statement gives us:
\( u = 20 \) mph
\( v = 25 \) mph
We can calculate the change in velocity: \( \Delta v = v - u = 25 - 20 = 5 \) mph.
Now we can find the acceleration:
\[ a = \frac{5 \text{ mph}}{0.5 \text{ h}} = 10 \text{ miles/hour}^2 \] This statement provides a unique value for acceleration. Thus, Statement (1) is sufficient.
Analyze Statement (2): "The particle increases its speed by 5 miles per hour."
This statement directly gives us the change in velocity:
\( \Delta v = v - u = 5 \) mph
We can find the acceleration using this information:
\[ a = \frac{\Delta v}{t} = \frac{5 \text{ mph}}{0.5 \text{ h}} = 10 \text{ miles/hour}^2 \] This statement also provides a unique value for acceleration. Thus, Statement (2) is sufficient.
Step 4: Final Answer:
Since each statement alone is sufficient to answer the question, the correct option is (D).