Question

Find the force needed to accelerate a mass of 40kg from velocity Vi=(4i-5j+3k)m/s to Vf=(8i+3j-5k)m/s in 10second.

Answer 1

The acceleration of the body

$$\vec a=\frac{\Delta \vec v}{\Delta t}=\frac{(8 {\bf i}+3{\bf j}-5{\bf k})-(4 {\bf i}-5{\bf j}+3{\bf k})}{10}=0.4 {\bf i}+0.8{\bf j}-0.8{\bf k}$$

The Newton's second law sates

$$\vec F=m\vec a$$ $$=40\times (0.4 {\bf i}+0.8{\bf j}-0.8{\bf k})=(16 {\bf i}+32{\bf j}-32{\bf k})\:\rm N$$