Understanding the Physics Principle

This problem involves the concepts of kinetic energy, work done, and force. The key principle connecting these is the Work-Energy Theorem.

• Work-Energy Theorem: The work done on an object is equal to the change in its kinetic energy. Mathematically, $W = \Delta KE$.
• Work done by a constant force: When a constant force $F$ acts on an object over a distance $d$ in the direction opposite to motion, the work done is $W = -F \cdot d$.
• Kinetic Energy: The energy an object possesses due to its motion, given by $KE = \frac{1}{2}mv^2$.

Applying the Concepts

We are given that both the lorry and the car have the same initial kinetic energy ($KE$) and are stopped by the same retarding force ($F$).

• Initial State: Let the initial kinetic energy for both be $KE_{initial} = KE$.
• Final State: Both vehicles come to rest, so their final kinetic energy is $KE_{final} = 0$.
• Change in Kinetic Energy: For both vehicles, $\Delta KE = KE_{final} - KE_{initial} = 0 - KE = -KE$.

Calculating Stopping Distance

Using the Work-Energy Theorem, the work done by the retarding force equals the change in kinetic energy.

• For the lorry: $W_{lorry} = \Delta KE \implies -F \cdot d_{lorry} = -KE$.
• For the car: $W_{car} = \Delta KE \implies -F \cdot d_{car} = -KE$.

From these equations, we can solve for the stopping distance ($d$):

• $d_{lorry} = \frac{KE}{F}$
• $d_{car} = \frac{KE}{F}$

Since both $KE$ (initial kinetic energy) and $F$ (retarding force) are the same for the lorry and the car, their stopping distances ($d$) must also be the same.

Conclusion

Both the lorry and the car will come to rest in the same distance because they possess the same initial kinetic energy and are acted upon by the same magnitude of retarding force.