$(a)$ Define work. State two factors on which the magnitude of work depends.
$(b)$ $A$ car and a truck have the same speed of $30 \, m/s$. If their masses are in the ratio $1:3$,find the ratio of their kinetic energy.

(1:3) Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. The magnitude of work depends on two factors: $(1)$ The magnitude of the force applied $(F)$ and $(2)$ The displacement of the object $(s)$ in the direction of the force.
$(b)$ Given: Speed of car $(v_1) = 30 \, m/s$,Speed of truck $(v_2) = 30 \, m/s$. Ratio of masses $(m_1 : m_2) = 1 : 3$.
Since kinetic energy $(E_k) = \frac{1}{2}mv^2$,the ratio of kinetic energies is:
$\frac{E_1}{E_2} = \frac{\frac{1}{2}m_1v_1^2}{\frac{1}{2}m_2v_2^2} = \frac{m_1}{m_2} \times \left(\frac{v_1}{v_2}\right)^2$
Since $v_1 = v_2$,the ratio becomes $\frac{m_1}{m_2} = \frac{1}{3}$.
Therefore,the ratio of kinetic energy is $1:3$.