A particle of potential energy shown in graph is moving towards right. The initial kinetic energy of particle is 21 J at x = 0. Mark the correct option(s)
 

At 𝑥 = 1, slope of the curve 𝑑𝑈/𝑑𝑥 = 0 ⇒ 𝐹 = −(𝑑𝑈/𝑑𝑥) = 0 ⇒ 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 0. 

The body is accelerating between (0 ≤ 𝑥 < 1), but not at 𝑥 = 1. Hence (A) is wrong.

At 𝑥 = 1, 𝑈 is maximum, hence kinetic energy is minimum. (B) is correct.

At 𝑥 = 0: 𝑈 = 0 and 𝐾 = 21 𝐽 ⇒ 𝐸 = 𝑈 + 𝐾 = 21 𝐽.

Hence at 𝑥 = 3 𝑚: 𝑈 = −20 𝐽; 𝐸 = 21 𝐽 ⇒ 𝐾 = 𝐸 − 𝑈 = 21 − (−20) = 41 𝐽. (C) is correct.

If the particle is trapped within 0 < 𝑥 ≤ 4 m, it must stop at some point and go back. But minimum kinetic energy of the particle is 1 J (at 𝑥 = 1 𝑎𝑛𝑑 𝑥 = 3). Hence it is not trapped in this range. (D) is wrong.