The position vector of a particle changes with time according to the relation $$\overrightarrow r (t) = 15{t^2}\widehat i + (4 - 20{t^2})\widehat j$$
What is the magnitude of the acceleration at t = 1 ?

The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

Ship A is sailing towards north-east with velocity $$\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge $$ km/hr where $$\mathop i\limits^ \wedge $$ points east and $$\mathop j\limits^ \wedge $$ , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in :