Question 1

What are the suvat equations and when do I use them?

Accepted Answer

The suvat equations are five formulas that relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) for motion with constant acceleration. They are: v = u + at, s = ut + ½at², s = ½(u+v)t, v² = u² + 2as, and s = vt - ½at². Use them when acceleration is constant, such as free fall under gravity or a car braking uniformly. Always list the knowns and the unknown you need, then pick the appropriate equation.

Question 2

How do I solve projectile motion problems in A-Level Maths?

Accepted Answer

For projectile motion, treat horizontal and vertical motion separately. The horizontal acceleration is zero (constant velocity), and vertical acceleration is -g (usually 9.8 m/s² downward). Use suvat equations for each direction. Write initial velocity components as u_x = u cosθ and u_y = u sinθ. Then find time of flight, maximum height, and range. Remember that at the highest point, vertical velocity is zero. Always use consistent sign conventions.

Question 3

What is the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity that measures how fast an object is moving, regardless of direction. Velocity is a vector quantity that includes both speed and direction. For example, a car moving at 30 m/s north has a velocity of 30 m/s north; if it turns and moves at 30 m/s east, its speed is still 30 m/s but its velocity has changed. In calculations, velocity can be positive or negative depending on the chosen direction.

Question 4

How do I find displacement from a velocity-time graph?

Accepted Answer

The displacement is the area under the velocity-time graph. For straight-line segments, calculate the area of rectangles, triangles, or trapezoids. If the graph goes below the time axis (negative velocity), the area is negative, indicating displacement in the opposite direction. The total displacement is the net area (sum of positive and negative areas). For curved graphs, you may need to integrate the velocity function.

Question 5

What does it mean if acceleration is negative?

Accepted Answer

Negative acceleration means acceleration in the negative direction relative to your chosen positive direction. It does not necessarily mean the object is slowing down. For example, if you choose upward as positive, a ball thrown upward has negative acceleration due to gravity (-9.8 m/s²) while moving upward (slowing down) and also while falling downward (speeding up in the negative direction). Always interpret signs in context.

Question 6

How do I handle variable acceleration in kinematics?

Accepted Answer

When acceleration is not constant, use calculus. Acceleration is the derivative of velocity with respect to time: a = dv/dt. Velocity is the derivative of displacement: v = ds/dt. To find velocity from acceleration, integrate a(t) with respect to t and use initial conditions to find the constant. To find displacement from velocity, integrate v(t) with respect to t. For example, if a(t) = 6t, then v(t) = ∫6t dt = 3t² + C, and if v(0)=2, then C=2.

Q: Kinematics

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Related Topics in AQA vocational Mathematics

A: Proof

B: Algebra and functions

C: Coordinate geometry in the ( x , y ) plane

D: Sequences and series

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