Newton's second law in a straight lineEdexcel A-Level Maths: Subtopic test

1. 1
   A sledge of mass $40$ kg is pulled from rest along horizontal ground by a horizontal rope. The tension in the rope is $100$ N and the resistance to motion is a constant $20$ N. Model the sledge as a particle.

   (a)

   Find the acceleration of the sledge.

   [1 mark]

   • A$2$ m s$^{-2}$
   • B$2.5$ m s$^{-2}$
   • C$3$ m s$^{-2}$
   • D$0.5$ m s$^{-2}$

   (b)

   Find the speed of the sledge $6$ s after it starts from rest.

   [1 mark]

   • A$36$ m s$^{-1}$
   • B$12$ m s$^{-1}$
   • C$18$ m s$^{-1}$
   • D$15$ m s$^{-1}$

   (c)

   Find the distance travelled by the sledge in these $6$ s.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle $P$ of mass $2$ kg is acted on by two forces only, $\mathbf{F}_1=(6\mathbf{i}-4\mathbf{j})$ N and $\mathbf{F}_2=(2\mathbf{i}+8\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.

   (a)

   Find the resultant force acting on $P$.

   [1 mark]

   • A$(4\mathbf{i}-12\mathbf{j})$ N
   • B$(8\mathbf{i}+12\mathbf{j})$ N
   • C$(8\mathbf{i}+4\mathbf{j})$ N
   • D$(4\mathbf{i}+2\mathbf{j})$ N

   (b)

   Find the acceleration of $P$.

   [1 mark]

   • A$(8\mathbf{i}+4\mathbf{j})$ m s$^{-2}$
   • B$(16\mathbf{i}+8\mathbf{j})$ m s$^{-2}$
   • C$(3\mathbf{i}-2\mathbf{j})$ m s$^{-2}$
   • D$(4\mathbf{i}+2\mathbf{j})$ m s$^{-2}$

   (c)

   Find the magnitude of the acceleration of $P$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lorry of mass $8000$ kg travels along a straight horizontal road. The resistance to the lorry's motion is a constant $1200$ N. Model the lorry as a particle.

   (a)

   The driving force of the lorry's engine is $6400$ N. Find the acceleration of the lorry.

   [3 marks]

   (b)

   The lorry is travelling at $13$ m s$^{-1}$ when the driver switches off the engine. The resistance remains $1200$ N. Find the distance the lorry travels from this moment until it comes to rest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ of mass $0.5$ kg moves in a horizontal plane under the action of two constant forces only, $\mathbf{F}_1=(4\mathbf{i}+p\mathbf{j})$ N and $\mathbf{F}_2=(q\mathbf{i}-3\mathbf{j})$ N, where $p$ and $q$ are constants and $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors. At time $t=0$ the velocity of $P$ is $(2\mathbf{i}+\mathbf{j})$ m s$^{-1}$, and at time $t=4$ s its velocity is $(10\mathbf{i}-3\mathbf{j})$ m s$^{-1}$.

   (a)

   Find the values of $p$ and $q$.

   [6 marks]

   (b)

   At $t=4$ the force $\mathbf{F}_2$ stops acting, and $\mathbf{F}_1$ continues to act alone. Find the speed of $P$ at $t=6$.

   [6 marks]

   Total for question 4: 12 marks

End of questions