We'll assume for the moment that once the train reaches its cruising speed and stops accelerating, it will maintain that speed. When a train standing at a platform in a station starts to move and gather speed, it accelerates in the direction of travel. The SI unit of acceleration is metres per second per second or metres per second squared ( m s -2). In mathematical terms, acceleration is the derivative of velocity with respect to time, and the second derivative of position with respect to time.Īcceleration is a vector quantity (it has both magnitude and direction). Note that if the velocity's magnitude is changing, it is accelerating regardless of whether the magnitude is increasing or decreasing (we all speak colloquially about deceleration on occasion, but the term is not generally used by physicists). It could describe a change in either the magnitude of the velocity or the direction of the velocity, or both. This sounds like a contradiction in terms, especially considering that we use the term “geostationary” to describe many of these satellites, but we'll see in due course why it really is the case that these orbiting objects are accelerating.Īcceleration describes the rate of change of velocity with respect to time. The Moon, for example, is accelerating, as are all of the World's orbiting satellites. There are also some not so obvious examples of acceleration, most of which you can see in the night sky, either with the naked eye or with the aid of a telescope. All of these things are examples of things that are accelerating. We may even be fortunate enough to witness the launch of a NASA or ESA space mission. A train leaving a platform, a car pulling away from a set of traffic lights, an aircraft taking off, or an apple falling from a tree. We can see examples of objects that are accelerating all around us. An object that is accelerating due to a gravitational force, but has no other forces acting upon it, is said to be in free fall. The result of the net force acting on the object is called acceleration. In order for the object's speed or direction to change, it must experience a net force in some direction. it moves at a constant speed in a straight line). This is why we use the average time and average velocity when calculating the acceleration.We have seen that an object in an inertial frame of reference is either at rest or has a constant velocity (i.e. As shown in Figure 2, the instantaneous velocity and the calculated average velocity have the same value at this average time, t 23. So when we take the average of t 2 and t 3, we find the time at the halfway point. The average of two points is the midpoint of the two points. The average velocities intersect with the instantaneous velocities at the midpoint of the two time measurements. Now consider the velocity versus time version of this graph shown in Figure 2. The average velocity between two points ( x 1, t 1) and ( x 2, t 2) is given by the slope of the straight line connecting these two points. If we were to measure the position of the object over smaller time intervals, we would see a smoother curve as indicated by the blue curve. Here we can draw a graph where we connect the points with the solid lines indicated by the red lines in Figure 1b. Figure 1b shows a plot of position versus time for an object moving with increasing velocity.
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