Kinetic and potential energy, work-energy theorem

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m. If \(F_A\) and \(F_B\) are the forces applied by the breaks on cars A and B, respectively, then the ratio \(F_A/F_B\) is

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec E\). Due to the force \(q\vec E\), its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s\(^2\). The work done by the (i) gravitational force and the (ii) resistive force of air is :

A body of mass 1 kg begins to move under the action of a time dependent force \(\vec{F} = (2t\,\hat{i} + 3t^2\,\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\) axis. What power will be developed by the force at the time t ?