## Calculus 8th Edition

a) $2ma i+6mbtj; 0\leq t \leq 1$ b) $2ma^2+\dfrac{9mb^2}{2}$
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) $W=\int_A^B F\cdot dr=\int_0^1 \lt 2ma, 6m bt \gt \cdot \lt 2at, 3bt^2 \gt dt$ $=\int_0^1 4ma^2 +18mb^2t^3 dt$ $=2m[a^2t^2+\dfrac{b^2t^4}{4}]_0^1$ $=2ma^2+\dfrac{9mb^2}{2}$