A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Weight and Motion in a Straight Line Under Gravity — mark scheme explained
The short answer
In AQA A-Level Mathematics, understanding weight and motion in a straight line under gravity is crucial. This involves the concepts of gravitational acceleration ( g ) and its value in SI units to varying degrees of accuracy.
The question
A ball is dropped from a height of 45 meters. Calculate the time it takes to reach the ground. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Use the equation s = ½gt 2 where s = 45 m and g = 9.81 m/s 2 .
- S2
Rearrange to solve for time: t = √(2s/g) .
- S3
Substitute the values: t = √(2 × 45 / 9.81) ≈ 3.03 s .
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Use the equation s = ½gt 2 where s = 45 m and g = 9.81 m/s 2 .
- S2
Rearrange to solve for time: t = √(2s/g) .
- S3
Substitute the values: t = √(2 × 45 / 9.81) ≈ 3.03 s .
Final answer: 3.03 seconds
Common mistakes
- Using the wrong value for gravitational acceleration g . — Always check the problem statement to see if a specific value of g is given. If not, use 9.81 m/s 2 as a standard value.
- Forgetting to consider the direction of motion when using kinematic equations. — Always define a positive direction (e.g., upwards) and use consistent signs for all variables. For example, if an object is thrown upwards, the initial velocity u is positive, and the acceleration due to gravity g is negative.
- Confusing weight with mass. — Remember that weight W is the force due to gravity and is calculated as W = mg . Mass m is a scalar quantity measured in kilograms (kg).
- Using incorrect units for weight, mass, or gravitational acceleration. — Always use consistent units. Weight is measured in newtons (N), mass in kilograms (kg), and gravitational acceleration in meters per second squared (m/s 2 ).
- Failing to consider the initial conditions when solving kinematic problems. — Always identify and use the given initial conditions (e.g., initial velocity u , initial displacement s 0 ) in your calculations. For example, if an object is dropped from rest, the initial velocity u is zero.
Where the marks go
- Full worked solution (all marking points)3 marks