Question

5. If a particle is moving with a displacement x= 5bt^2+t^3/3.
Find the velocity of particle?​

Answer 1

Answer:

$x = 5b {t}^{2} + {t}^{ \frac{3}{3} }$

$we \: know \: that \: , \\ v = \frac{dx}{dt}$

there for,

$v = \frac{d}{dt} (5b {t}^{2} + {t}^{ \frac{3}{3} } ) \\ = > v = 10b {t}^{(2 - 1)} + { \frac{3}{3} t}^{ (\frac{3}{3} - 1)} \\ = > v = 10b {t}^{1} + \frac{3}{3} {t}^{( \frac{3 - 3}{3} )} \\ = > v = 10bt$

hence, velocity of the partial is 10bt.