A train with an initial velocity of 20$ms^{-1}$ is subjected to a uniform deceleration of 2m-2. The time required to bring the train to a complete halt is?

Analyze the question: The train starts at 20 m/s and slows uniformly at 2 m/s² (the "2m-2" in the question is a typo for 2 ms⁻²). We need the time it takes to stop, which means the final velocity is 0.

Concept: For uniform acceleration, use the first equation of motion:

v = u + at

For deceleration, the acceleration is negative.

Solution:

Given:

• u = 20 m/s
• v = 0 m/s (comes to a halt)
• a = -2 m/s² (deceleration)

Substitute:

0 = 20 + (-2)t

0 = 20 - 2t

2t = 20

t = 20 ÷ 2 = 10 s

Check: The velocity drops by 2 m/s every second. Starting from 20 m/s, it takes 20 ÷ 2 = 10 seconds to reach zero.

Answer: B. 10 s

Tip: In "come to rest/halt" questions, always set v = 0. Also, deceleration means a negative acceleration. A quick shortcut for stopping time is t = u ÷ a (initial speed divided by deceleration). Also check the units: the deceleration should be in m/s², and the question's "m-2" is just a typing slip.