Two particles P and Q, of masses 0.3kg and 0.2kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4ms⁻¹ directly towards Q. After P and Q collide, Q begins to move with a speed of 3 ms⁻¹. After the collision, Q moves directly towards a third particle R, of mass mkg, which is at rest on the plane. The two particles Q and R coalesce on impact and move with a speed of 2ms⁻¹.

A car of mass 900 kg is moving on a straight horizontal road ABCD. There is a constant resistance of magnitude 800 N …

A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving…

A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the poi…

The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.

The variables x and θ satisfy the differential equation x cos² θ (dx/dθ) = 2 tan θ + 1, for 0 ≤ θ < ½π and x > 0. It …

By sketching suitable graphs, show that the equation e²ˣ = 6 + e⁻ˣ has exactly one real root.