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  4. The acceleration a of the body starting from rest varies with time following the equation a =8 t +5 . The velocity of the body at time t=2 sec will be:

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Q. The acceleration $a$ of the body starting from rest varies with time following the equation $a =8 t +5 .$ The velocity of the body at time $t=2$ sec will be:

Motion in a Straight Line

Solution:

$a=8 t+5 \Rightarrow \frac{d v}{d t}=8 t+5 \Rightarrow d v=(8 t+5) d t$
$\int_{0}^{v} d v=\int_{0}^{t}(8 t+5) d t \Rightarrow v=\frac{8 t^{2}}{2}+5 t$
$v=4 t^{2}+5 t=4 \times 4+10=16+10=26 m / s$