Quantities and S.I. units in mechanicsEdexcel A-Level Maths: Subtopic test

1. 1
   A car of mass 1200 kg travels along a straight horizontal road at a constant $72$ km h$^{-1}$.

   (a)

   What is the speed of the car in m s$^{-1}$?

   [1 mark]

   • A$1.2$ m s$^{-1}$
   • B$20$ m s$^{-1}$
   • C$259.2$ m s$^{-1}$
   • D$1200$ m s$^{-1}$

   (b)

   How far does the car travel in 30 s?

   [1 mark]

   • A$2160$ m
   • B$2.4$ m
   • C$600$ m
   • D$18\,000$ m

   (c)

   Find the weight of the car, taking $g=9.8$ m s$^{-2}$, and state its unit.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A cyclist of mass 70 kg travels a distance of 5.4 km in a time of 15 minutes along a straight track at a constant speed.

   (a)

   What is the cyclist's speed in m s$^{-1}$?

   [1 mark]

   • A$0.36$ m s$^{-1}$
   • B$1.5$ m s$^{-1}$
   • C$90$ m s$^{-1}$
   • D$6$ m s$^{-1}$

   (b)

   What is the cyclist's speed in km h$^{-1}$?

   [1 mark]

   • A$21.6$ km h$^{-1}$
   • B$0.36$ km h$^{-1}$
   • C$81$ km h$^{-1}$
   • D$324$ km h$^{-1}$

   (c)

   Find the weight of the cyclist, taking $g=9.8$ m s$^{-2}$, and express the unit of weight in terms of the S.I. base units kg, m and s.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A stone of mass 0.4 kg is dropped from the top of a cliff and hits the sea at a speed of $29.7$ m s$^{-1}$. The stone is modelled as a particle moving vertically under gravity only.

   (a)

   State three modelling assumptions that are being made about the stone and its motion.

   [3 marks]

   (b)

   Convert the impact speed to km h$^{-1}$, giving your answer to 3 significant figures, and find the weight of the stone, taking $g=9.8$ m s$^{-2}$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student walks towards a door at $5.4$ km h$^{-1}$ for 4 s and then pushes the door with a constant force of 40 N, applied perpendicular to the door at its outer edge, which is 0.9 m from the hinge. The door has mass 25 kg. Take $g=9.8$ m s$^{-2}$.

   (a)

   (i) Calculate the moment of the force about the hinge and state its unit.
   (ii) Express the unit of moment in terms of the S.I. base units kg, m and s.
   (iii) Find the weight of the door.

   [6 marks]

   (b)

   (i) Convert the student's walking speed to m s$^{-1}$.
   (ii) Find the distance the student walks in the 4 s.
   (iii) State two modelling assumptions made when the push is modelled as a constant 40 N force perpendicular to the door.

   [6 marks]

   Total for question 4: 12 marks

End of questions