Constant Acceleration Formulae

Understanding Constant Acceleration Formulae

  • Constant acceleration refers to a situation where an object’s acceleration does not change over time. In essence, the object is either continuously speeding up or slowing down at a constant rate.
  • There are several key formulae related to constant acceleration, often known as the equations of motion or SUVAT equations. SUVAT is an acronym representing five key quantities: displacement(S), initial velocity(U), final velocity(V), acceleration(A), and time(T).

Key SUVAT Equations

  • First equation: V = U + AT. This formula is derived from the definition of acceleration. It states that the final velocity(V) is equal to the initial velocity(U) plus the product of acceleration(A) and time(T).
  • Second equation: S = UT + 1/2 AT². This equation calculates the displacement or distance travelled(S) under constant acceleration. It’s the sum of the product of the initial velocity and time, and half the product of acceleration and time squared.
  • Third equation: V² = U² + 2AS. In this formula, the square of the final velocity equals the square of the initial velocity plus twice the product of acceleration and displacement. This equation is useful when time is unknown or not required.

Solving Problems with SUVAT Equations

  • When solving problems, remember to check the units of all given and required quantities. They should be consistent with one another. Commonly, SI units are used: m/s for speed or velocity, m/s² for acceleration, and s for time.
  • In some situations, not all five SUVAT quantities are known or required. When this occurs, you need to select the correct equations that use only the known quantities and will allow you to calculate the unknown one.
  • It’s critical to understand the direction of motion and the sign convention you are using. If motion in one direction is taken as positive, motion in the opposite direction must be taken as negative.
  • Investigate the shape and nature of the graphs representing motion under constant acceleration. Displacement-time graphs are typically parabolic, velocity-time graphs are linear, and acceleration-time graphs are horizontal lines (if acceleration is constant).

Constant Acceleration in a Vertical Context

  • When an object is in free fall or thrown upwards, the only force acting on the object (ignoring air resistance) is gravity. This force imparts an acceleration of approximately -9.8 m/s² (downwards). The negative sign indicates direction.
  • Even in vertical motion scenarios, the SUVAT equations still apply. The term ‘displacement’ now represents vertical height, and ‘velocity’ indicates vertical speed (upwards positive, downwards negative).