EQUATIONS OF UNIFORMLY ACCELERATED MOTION

CONTENT

1. Velocity – Time v-t Graph
2. Relative Motion
3. Derivations of Equation of Uniformly Accelerated Motion
4. Derivation of Equations of Uniform Motion
5. Application of the Equations of Uniform Accelerating Bodies
6. Motion of Bodies Under Gravity

Velocity – Time v-t Graph

1. Gradient of a v-t graph = acceleration

\(acceleration = gradient \\ = {\text{change in velocity} \over \text{change in time}} \\ acceleration (a) = \frac{Δv}{Δt}\)

2. Area under a v-t graph = distance.

1. Total distance covered during the motion = area of trapezium 0edc
2. Distance covered during acceleration = area of triangle 0ea
3. Distance covered during constant velocity = area of rectangle aedb
4. Distance covered during deceleration = area of triangle bdc
5. Acceleration = slope of line 0e, \(a = \frac{ae}{0a}\)
6. Deceleration =  slope of dc, \(-a = \frac{bd}{bc}\)

Example 1:

A car starts from rest and accelerates uniformly to 15ms^-1 in 5 s.