Question

Initial velocity of a particle is $u$ at time $t = 0$. If acceleration $f$ of the particle is given by at, then the valid relation is

• A. $\upsilon=u+at$
• B. $\upsilon=u+\frac{1}{2}at^2$
• C. $\upsilon=u+at^2$
• D. $\upsilon=u$

Answer 1

Answer: (B)

$\upsilon=u+\frac{1}{2}at^2$

Answer 2

$f = \frac{d \upsilon}{dt} = at$ i.e. $d \, \upsilon = at \, dt$ $\int\limits^{\upsilon}_{\upsilon} d \, \upsilon = \int\limits^t_0 \, at \, dt$ i.e. $\upsilon - u = \frac{1}{2} at^2$ i.e. $\upsilon =u + \frac{1}{2} at^2$