Moderate -0.8 This is a straightforward dimensional analysis question requiring students to verify that each term has dimensions of length. While it's a Further Maths mechanics question, it only requires basic knowledge that displacement has dimensions [L], velocity [LT⁻¹], acceleration [LT⁻²], and time [T]. The verification is routine with no problem-solving or insight needed—just systematic checking that ut and gt²/2 both give [L].
A ball is thrown vertically upwards with speed \(u\) so that at time \(t\) its displacement \(s\) is given by the formula
$$s = ut - \frac{gt^2}{2}$$
Use dimensional analysis to show that this formula is dimensionally consistent.
Fully justify your answer.
[4 marks]
Question 5:
5 | Recalls the dimensions for
displacement, velocity, time and
acceleration due to gravity | 1.2 | B1 | [𝑠𝑠] = 𝐿𝐿
−1
[𝑢𝑢] = 𝐿𝐿𝑇𝑇
[𝑡𝑡] = 𝑇𝑇
−2
½ is [dgi]m=en𝐿𝐿s𝑇𝑇ionless
[ ] =
−1 =
𝑢𝑢2𝑡𝑡 𝐿𝐿𝑇𝑇 𝑇𝑇 = 𝐿𝐿
g𝑡𝑡 −2 2
� 2 � = 𝐿𝐿𝑇𝑇 𝑇𝑇 𝐿𝐿
[ ] =
2
g𝑡𝑡
𝑢𝑢𝑡𝑡 � 2 � = [𝑠𝑠] = 𝐿𝐿
So formula is dimensionally
consistent
Explains that ½ or 2 is a
dimensionless quantity in the
given equation | 2.4 | E1
Substitutes ‘their’ dimensions
into the expressions and gt2 | 1.1a | M1
𝑢𝑢𝑡𝑡
Completes a reasoned
argument using dimensions to
verify that the dimensions of
and and s are all equal to L
2 𝑢𝑢𝑡𝑡
g𝑡𝑡
and concludes that the formula
2
is dimensionally consistent
R1 is not dependent on E1 | 2.1 | R1
Total | 4
Q | Marking instructions | AO | Marks | Typical solution
A ball is thrown vertically upwards with speed $u$ so that at time $t$ its displacement $s$ is given by the formula
$$s = ut - \frac{gt^2}{2}$$
Use dimensional analysis to show that this formula is dimensionally consistent.
Fully justify your answer.
[4 marks]
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2021 Q5 [4]}}