Speed of a particle moving in a straight line varies with time as v = (3 + 2t) m/s. The distance covered in first 3 second is

Question

Speed of a particle moving in a straight line varies with time as v = (3 + 2t) m/s. The distance covered in first 3 second is (A) 24 m (B) 27 m (C) 18 m (D) 9 m

Tardigrade Admin · Accepted Answer

v = 3+ 2t dx= vdt dx = (3+ 2t)dt ∫ dx = ∫(3+2t)dt xf -xi = [3t+(2t2/2)]03 s = (3×3 +32)-0 s= 18 m

Q. Speed of a particle moving in a straight line varies with time as $v = (3 + 2 t) m / s$ . The distance covered in first $3$ second is

$24 m$

$27 m$

$18 m$

$9 m$

$v = 3 + 2 t$
$d x = v d t$
$d x = (3 + 2 t) d t$
$\int d x = \int (3 + 2 t) d t$
$x_{f} - x_{i} = [3 t + \frac{2 t ^{2}}{2}]_{0}^{3}$
$s = (3 \times 3 + 3^{2}) - 0$
$s = 18 m$

Q. Speed of a particle moving in a straight line varies with time as v=(3+2t)m/s. The distance covered in first 3 second is

24m

27m

18m

9m