Question

A block of mass 2 kg is kept at origin at t = 0 and is having velocity $4 \sqrt { 5 }$m/s in positive x-direction. The only force on it is a conservative and its potential energy is defined as U = – x³ + 6x² + 15 (SI units). Its velocity when the force acting on it is minimum (after the time t = 0) is –

• A. 8 m/s
• B. 4 m/s
• C. $10 \sqrt { 24 }$m/s
• D. None of these

Answer 1

Answer: (A)

8 m/s

Answer 2

x = 0

K = $\frac { 1 } { 2 } \times 2 \times 80$ =

80 J and U = 15J

\ E = K + U = 95 J

F = $\frac { - \mathrm { dU } } { \mathrm { dx } }$Ž

F = 3x² – 12x

For F = minimum, = 0

Ž x = 2 m

At x = 2m

E = K + U

Ž 95 = $\frac { 1 } { 2 } \times 2 \times v ^ { 2 }$+ (–8 + 24 + 15)

Ž v = 8 m/s