Question

A particle starts with initial velocity 2.5 m/s along the x direction and accelerates
uniformly at the rate 50 cm/s2
. Find time taken to increase the velocity to 7.5 m/s.​

Answer 1

$\large \underline \bold{Given}$:-

$\: \: \: \:$$\sf{initial \: velocity \: (u) = 2.5 \: m/s}$

$\: \: \: \: \: \: \:$$\sf{acceleration \: (a) = 0.5 \: m/s^{2}}$

$\: \: \: \:$$\sf{Final \: velocity \: (v) = 7.5 \: m/s}$

$\large \underline \bold{To \: Find}$:-

$\:$$\sf{how \: much \: time \: taken \: by \: the \: particle \: ?}$

$\large \underline \bold{Using \: Formula}$:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$$\sf\boxed{\sf\red{a = \dfrac{(v - u)}{t}}}$

here ,

$\: \: \: \: \: \: \: \: \: \: \:$ $\sf{a \: = \: acceleration}$

$\: \: \: \: \: \: \: \: \: \: \:$ $\sf{u \: = \: initial \: \: velocity}$

$\: \: \: \: \: \: \: \: \: \: \:$ $\sf{v \: = \: final \: \: velocity}$

$\: \: \: \: \: \: \: \: \: \: \:$ $\sf{t \: = \: time \: taken}$

$\large \underline \bold{Solution}$:-

$\: \:$$\sf{On \: using \: the \: above \: formula}$-

$\: \: \: \: \: \: \: \: \:$$\sf{t \: =\: \dfrac{(v - u)}{a}}$

$\: \: \: \: \: \: \: \: \:$$\sf{t \: = \: \dfrac{(7.5 - 2.5)}{0.5}}$

$\: \: \: \: \: \: \: \: \:$$\sf{t \: = \: \dfrac{5}{0.5}}$

$\: \: \: \: \: \: \: \: \:$$\large \bold{t \: = \: 10 \: second}$

$\sf{The \: particle \: took \: 10 \: seconds \: \: to \: increase \: the \: velocity.}$