A particle starts with an initial velocity of 10.0 ms⁻¹ along x-direction and accelerates uniformly at the rate of 2.0 ms⁻². The time taken by the particle to reach the velocity of 60.0 ms⁻¹ is __________.

Solution

Physics sir · 3 steps

Acceleration is the gain in speed per second, so find how much speed it must gain.

1. Pick the equation. We know u, v and a, and we want t. The equation that links exactly these four is v = u + at.

   t = (v - u)/a = (60 - 10)/2 s

2. Put in numbers. The particle must gain 60 - 10 = 50 m s⁻¹. At 2 m s⁻² it gains 2 m s⁻¹ every second, so this takes 50 ÷ 2 = 25 s.
3. So. The time taken is 25 s, option (d).

The idea to keep. Under uniform acceleration, time equals the change in velocity divided by the acceleration. Always subtract the starting velocity first.

Answer from the NTA final answer key. Solution by PrepWiser.