Question

If the velocity of a particle is given by $v = ( 180 - 16 x ) ^ { 1 / 2 }$ m/s, then its acceleration will be

• A. Zero
• B. 8 m/s²
• C. – 8 m/s²
• D. 4 m/s²

Answer 1

Answer: (C)

– 8 m/s²

Answer 2

$v = ( 180 - 16 x ) ^ { 1 / 2 }$

As $a = \frac { d v } { d t } = \frac { d v } { d x } \cdot \frac { d x } { d t }$

$\therefore a = \frac { 1 } { 2 } ( 180 - 16 x ) ^ { - 1 / 2 } \times ( - 16 ) \left( \frac { d x } { d t } \right)$

$= - 8 ( 180 - 16 x ) ^ { - 1 / 2 } \times v$

$= - 8 ( 180 - 16 x ) ^ { - 1 / 2 } \times ( 180 - 16 x ) ^ { 1 / 2 }$ $= - 8 \mathrm {~m} / \mathrm { s } ^ { 2 }$