Quantities and units in mechanicsAQA A-Level Maths: Subtopic test

1. 1
   A crate of mass $15$ kg rests on a table. Take $g=9.8$ m s$^{-2}$ on Earth.

   (a)

   Find the weight of the crate.

   [1 mark]

   • A$147$ N
   • B$1.53$ N
   • C$15$ N
   • D$147$ kg

   (b)

   Which of these is the unit of weight expressed in SI base units?

   [1 mark]

   • Akg m s$^{-1}$
   • Bkg m$^2$ s$^{-2}$
   • Ckg m s$^{-2}$
   • Dm s$^{-2}$

   (c)

   The crate is taken to the Moon, where $g=1.6$ m s$^{-2}$. State its mass and find its weight there.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A cyclist travels $1.2$ km in $4$ minutes at a constant speed along a straight road.

   (a)

   Find the speed of the cyclist in m s$^{-1}$.

   [1 mark]

   • A$0.3$ m s$^{-1}$
   • B$5$ m s$^{-1}$
   • C$300$ m s$^{-1}$
   • D$18$ m s$^{-1}$

   (b)

   Express the speed of the cyclist in km h$^{-1}$.

   [1 mark]

   • A$1.8$ km h$^{-1}$
   • B$5$ km h$^{-1}$
   • C$300$ km h$^{-1}$
   • D$18$ km h$^{-1}$

   (c)

   The cyclist then speeds up uniformly from $5$ m s$^{-1}$ to $8$ m s$^{-1}$ in $6$ s. Find the acceleration, including its unit.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A trolley of mass $8$ kg is pulled across a smooth horizontal floor by a resultant horizontal force of $20$ N. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the acceleration of the trolley, and show that the unit you use for acceleration is consistent with $1$ N being $1$ kg m s$^{-2}$.

   [3 marks]

   (b)

   Extra load is added and the resultant force is doubled. The acceleration is now $4$ m s$^{-2}$. Find the new mass of the trolley and its weight on Earth.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A ball is dropped from rest from a height $h$ metres. The time $T$ seconds it takes to reach the ground is modelled by $T=\sqrt{\dfrac{2h}{g}}$, where $g$ is the acceleration due to gravity in m s$^{-2}$. On Earth take $g=9.8$ m s$^{-2}$. The speed $v$ on landing is given by $v=gT$.

   (a)

   (i) Show that the formula for $T$ is consistent in its units.
   (ii) Find $T$ when $h=19.6$ m on Earth.
   (iii) Find the landing speed in m s$^{-1}$ and in km h$^{-1}$.

   [6 marks]

   (b)

   The same ball (mass $0.4$ kg) is dropped from $19.6$ m on another planet and takes $4$ s to reach the ground.
   (i) Find $g$ for that planet.
   (ii) Find the weight of the ball on that planet and on Earth, and say whether the mass of the ball changes.

   [6 marks]

   Total for question 4: 12 marks

End of questions