Answer
a) $2ma i+6mbtj; 0\leq t \leq 1$ b) $2ma^2+\dfrac{9mb^2}{2}$
Work Step by Step
a) $r'(t)=\lt 2at, 3b t^2 \gt ; r''(t) \lt 2a , 6bt \gt $
Since, $F=m r''(t)$
$F=\lt 2ma, 6m bt \gt$
$F=2ma i+6mbtj$ and $ 0\leq t \leq 1$
b) $W=\int_A^B F\cdot dr=\int_0^1 \lt 2ma, 6m bt \gt \cdot \lt 2at, 3bt^2 \gt dt$
$=\int_0^1 4ma^2 +18mb^2t^3 dt$
$=2m[a^2t^2+\dfrac{b^2t^4}{4}]_0^1$
$=2ma^2+\dfrac{9mb^2}{2}$
