A crate of mass 500 kg is being pulled along rough horizontal ground by a horizontal rope attached to a winch. The winch produces a constant pulling force of 2500 N and the crate is moving at constant speed. Find the coefficient of friction between the crate and the ground.

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.