1.A $5\text{ kg}$ body is acted upon by a constant force of $20\text{ N}$. Find acceleration and velocity after $4\text{ s}$ starting from rest.
Sol: $a = \frac{F}{m} = \frac{20}{5} = 4\text{ m/s}^2$. Velocity $v = u + at = 0 + 4(4) = 16\text{ m/s}$.
2.State Newton's second law and show that $F = ma$.
Sol: Rate of change of momentum is proportional to applied force: $F \propto \frac{dp}{dt} = m \frac{dv}{dt} = ma$.
3.A block of mass $m=2\text{ kg}$ rests on a horizontal plane with coefficient of static friction $\mu_s = 0.4$. Find maximum static friction force.
Sol: Normal reaction $N = mg = 2(9.8) = 19.6\text{ N}$. Maximum static friction $f_s = \mu_s N = 0.4(19.6) = 7.84\text{ N}$.
4.Calculate tension $T$ in a rope lifting a mass of $10\text{ kg}$ upwards with acceleration $a=2\text{ m/s}^2$.
Sol: $T - mg = ma \implies T = m(g + a) = 10(9.8 + 2) = 118\text{ N}$.
