A-Level CAIE Mathematics AS 4.4 Newton's laws of motion Question Bank

A particle P is projected vertically upwards with speed $20 \mathrm{~m} \mathrm{~s}^{-1}$ from a point on the ground.

A particle of mass 0.2 kg moving in a straight line experiences a constant resistance force of 1.5 N . When the particle is moving at speed $2.5 \mathrm{~m} \mathrm{~s}^{-1}$, a constant force of magnitude $F \mathrm{~N}$ is applied to it in the direction in which it is moving. Given that the speed of the particle 5 seconds later is $4.5 \mathrm{~m} \mathrm{~s}^{-1}$, find the value of F.

Two particles A and B, of masses 0.8 kg and 0.2 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang vertically. The system is released from rest. Show that the acceleration of A has magnitude $6 \mathrm{~m} \mathrm{~s}^{-2}$ and find the tension in the string.

A particle of mass 0.2 kg is resting in equilibrium on a rough plane inclined at $20^{\circ}$ to the horizontal.

A block of mass 3 kg is initially at rest on a smooth horizontal floor. A force of 12 N , acting at an angle of $25^{\circ}$ above the horizontal, is applied to the block. Find the distance travelled by the block in the first 5 seconds of its motion.

A particle of mass 2 kg is initially at rest on a rough horizontal plane. A force of magnitude 10 N is applied to the particle at $15^{\circ}$ above the horizontal. It is given that 10 s after the force is applied, the particle has a speed of $3.5 \mathrm{~m} \mathrm{~s}^{-1}$.

Two particles P and Q, of masses 0.6 kg and 0.4 kg respectively, are connected by a light inextensible string. The string passes over a small smooth light pulley fixed at the edge of a smooth horizontal table. Initially P is held at rest on the table and Q hangs vertically (see diagram). P is then released. Find the tension in the string and the acceleration of Q.

A particle moves up a line of greatest slope of a rough plane inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha=0.28$. The coefficient of friction between the particle and the plane is $\frac{1}{3}$.

A straight ice track of length 50 m is inclined at $14^{\circ}$ to the horizontal. A man starts at the top of the track, on a sledge, with speed $8 \mathrm{~m} \mathrm{~s}^{-1}$. He travels on the sledge to the bottom of the track. The coefficient of friction between the sledge and the track is 0.02 . Find the speed of the sledge and the man when they reach the bottom of the track.

A block is at rest on a rough horizontal plane. The coefficient of friction between the block and the plane is 1.25 .