Question

A 10 kg object is acted on by a conservative force given by F = - 2x – 6x², with F in newtons and x in metres. If the object has a velocity of 4 m/s in the negative direction of the x – axis when it is at x = 4m, then its speed when it passes through the origin is:

• A. $\sqrt { \frac { 112 } { 3 } } \mathrm {~m} / \mathrm { s }$
• B. $\sqrt { \frac { 224 } { 5 } } \mathrm {~m} / \mathrm { s }$
• C. $\sqrt { \frac { 112 } { 5 } } \mathrm {~m} / \mathrm { s }$
• D. $\sqrt { \frac { 180 } { 5 } } \mathrm {~m} / \mathrm { s }$

Answer 1

Answer: (B)

$\sqrt { \frac { 224 } { 5 } } \mathrm {~m} / \mathrm { s }$

Answer 2

K = $\frac { 1 } { 2 }$ .10 . (-4)² = 80J

U = 16 + 2 × 64 = 16 + 128 = 144 J

E = 80 + 144 = 224 J

at x = 0, U = 0

E = K ⇒ $\frac { 1 } { 2 }$ mv² = 224

⇒ v = $\sqrt { \frac { 224 } { 5 } } \mathrm {~m} / \mathrm { s }$