Question

The initial velocity of a particle is $\boldsymbol { u }$ (at $t = 0$ )and the acceleration $f$ is given by at . Which of the following relation is valid

• A. $v = u + a t ^ { 2 }$
• B. $v = u + a \frac { t ^ { 2 } } { 2 }$
• C. $v = u + a t$
• D. $v = u$

Answer 1

Answer: (B)

$v = u + a \frac { t ^ { 2 } } { 2 }$

Answer 2

If acceleration is variable (depends on time) then

$v = u + \int ( f ) d t$ $= u + \int ( a t ) d t$ $= u + \frac { a t ^ { 2 } } { 2 }$