Speed, Velocity and Acceleration

Speed is not the same as velocity, speed is de ned as the rate of change of distance, whereas, velocity is the rate of change of displacement. Speed is a scalar and velocity is a vector. Acceleration is also a vector which is de ned as the rate of change of velocity.

Please note that this is not in the formula booklet.

1.2.2 Equations of Uniformly Accelerated Motion in a Straight Line

If acceleration is constant, the following equations of can be formed: From the de nition of acceleration:

1.2.3 Projectiles

A projectile is an object moving freely in a gravitational eld. 2-D projectiles can be analyzed, because, we know the vertical acceleration (−9.81ms−2) and that horizontal velocity does not change (no acceleration because there is no horizontal force). We also know that vertical velocity is 0 at maximum height. We can nd the range using:

1.2.4 Motion-time Graphs

For distance-time graphs, the gradient is the speed. So, a straight-line means a constant speed, an increasing gradient means accelerating, and a decreasing gradient means retardation. For speed-time graphs, the gradient is the acceleration and the area underneath the graph is the distance traveled. Displacement-time graphs are similar to distance-time graphs, except that they can have a negative `y-value’, this is because displacement is a vector and so can be negative. Velocity-time graphs are similar to speed-time graphs, but again, because velocity is a vector, the velocity can be negative. Examples: