A train with an initial velocity of 20$ms^{-1}$ is subjected to a uniform deceleration of 2$ms^{-2}$. 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 until it stops. We need the time taken to stop.

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

v = u + at

Deceleration means the acceleration is negative, so a = −2 m/s².

Solution:

Given:

• Initial velocity, u = 20 m/s
• Final velocity, v = 0 (the train comes to a complete halt)
• Acceleration, a = −2 m/s²

Substitute into v = u + at:

0 = 20 + (−2)t

0 = 20 − 2t

2t = 20

t = 20 ÷ 2 = 10 s

Check: In 10 s the speed drops by 2 × 10 = 20 m/s, taking it from 20 m/s to 0. ✓

Answer: The time required is 10 s, which is option B.

Tip: For "time to stop" questions, set v = 0 and use t = u/a (ignoring the sign). Here that is 20/2 = 10 s. Be careful not to pick 40 s (from multiplying 20 × 2) or 20 s (from forgetting to divide by the deceleration). Always check that the units cancel to seconds.