The most common example of this is uniform circular motion, where an object or particle moves in a circle at constant speed. In this case, the acceleration vector points to the centre of the circle. This is known as centripetal acceleration. See, for example:mancity said:Homework Statement: How would we define a value for acceleration if only the direction is changing and not the speed?
Relevant Equations: acceleration has both speed and direction
How would we define a value for acceleration if only the direction is changing and not the speed?
Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.
Acceleration is typically measured in meters per second squared (m/s^2) in the metric system or feet per second squared (ft/s^2) in the imperial system. It can also be measured using other units such as kilometers per hour squared (km/h^2) or miles per hour squared (mi/h^2).
If only the direction is changing, then the magnitude of the acceleration can be calculated by dividing the change in velocity by the time it took for the change to occur. This can be represented by the equation a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time.
Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how quickly the velocity is changing and in what direction.
Yes, acceleration can be negative. This means that the object is slowing down or changing direction in the opposite direction of its current velocity. For example, if an object is moving to the right with a velocity of 10 m/s and then starts moving to the left with a velocity of 5 m/s, its acceleration would be -5 m/s^2.