Question

A particle starting with an initial velocity \(2 \text{ ms}^{-1}\) moves with a uniform linear acceleration \(2 \text{ ms}^{-2}\). The particle velocities at the end of the 5 seconds and 10 seconds of its motion from the start, are in the ratio

• A. 1 : 2
• B. 11 : 16
• C. 6 : 11
• D. 2 : 1

Hint:

The ratio of velocities is not simply the ratio of times unless the initial velocity is zero. If \(u=0\), then \(v_1/v_2 = t_1/t_2 = 1/2\). Since \(u \neq 0\), the ratio shifts closer to 1.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For uniform linear acceleration, we use the first equation of motion: \(v = u + at\), where \(u\) is initial velocity, \(a\) is acceleration, and \(t\) is time.

Step 2: Detailed Explanation:
Given: \(u = 2 \text{ m/s}\), \(a = 2 \text{ m/s}^2\).
1. Velocity at \(t_1 = 5 \text{ s}\):
\[ v_1 = u + at_1 = 2 + (2 \times 5) = 2 + 10 = 12 \text{ m/s} \]
2. Velocity at \(t_2 = 10 \text{ s}\):
\[ v_2 = u + at_2 = 2 + (2 \times 10) = 2 + 20 = 22 \text{ m/s} \]
3. Finding the ratio:
\[ \text{Ratio} = \frac{v_1}{v_2} = \frac{12}{22} = \frac{6}{11} \]

Step 3: Final Answer:
The ratio of the velocities is 6 : 11.