← Mathematics of Mechanics syllabus

ScotlandMathematics of Mechanics

Linear and Parabolic Motion

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do Newton's laws relate force and motion, and how do you analyse equilibrium, friction, inclined planes and connected particles?

Apply Newton's three laws of motion; draw free-body diagrams; resolve forces; analyse equilibrium, friction, motion on inclined planes, and systems of connected particles.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on dynamics, covering Newton's three laws, free-body diagrams, resolving forces, equilibrium, friction with the coefficient of friction, motion on inclined planes, and connected-particle systems using the equation of motion F equals ma.
14 min answer →

How do you describe straight-line motion, and how do calculus and the constant-acceleration equations connect displacement, velocity and acceleration?

Work with rectilinear motion: relate displacement, velocity and acceleration by differentiation and integration, use the equations of motion for constant acceleration, and interpret motion-time graphs.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on rectilinear motion, linking displacement, velocity and acceleration through differentiation and integration, applying the constant-acceleration equations, and reading velocity-time and displacement-time graphs.
12 min answer →

How do you describe motion in two or three dimensions using vector functions, and how do you find relative velocity, closest approach and whether two bodies collide?

Use position, velocity and acceleration vectors as functions of time; calculate relative velocity; and find the closest approach of two moving bodies and the condition for collision.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on vector kinematics: differentiating and integrating position vectors, computing relative velocity and relative position, and finding the time and distance of closest approach or the condition for a collision.
13 min answer →

How do you model a projectile moving under gravity, and how do you find its range, maximum height, time of flight and path?

Model projectile motion under gravity by treating horizontal and vertical motion independently; find time of flight, range, maximum height, velocity at any time, and the equation of the parabolic path.
A focused answer to the SQA Advanced Higher Mathematics of Mechanics content on projectiles, resolving the initial velocity into horizontal and vertical parts, applying the constant-acceleration equations independently in each direction, and deriving time of flight, range, maximum height and the equation of the trajectory.
13 min answer →