      Protons in a linear accelerator are accelerated from rest to [latex] 2. What is the average acceleration of the protons? Instantaneous acceleration a , or acceleration at a specific instant in time , is obtained using the same process discussed for instantaneous velocity. The result is the derivative of the velocity function v t , which is instantaneous acceleration and is expressed mathematically as.Thus, similar to velocity being the derivative of the position function, instantaneous acceleration is the derivative of the velocity function. We can show this graphically in the same way as instantaneous velocity.In Figure , instantaneous acceleration at time t 0 is the slope of the tangent line to the velocity-versus-time graph at time t 0. Also in part a of the figure, we see that velocity has a maximum when its slope is zero. This time corresponds to the zero of the acceleration function. In part b , instantaneous acceleration at the minimum velocity is shown, which is also zero, since the slope of the curve is zero there, too.Thus, for a given velocity function, the zeros of the acceleration function give either the minimum or the maximum velocity. In view a , instantaneous acceleration is shown for the point on the velocity curve at maximum velocity. At this point, instantaneous acceleration is the slope of the tangent line, which is zero.At any other time, the slope of the tangent line—and thus instantaneous acceleration—would not be zero. First, a simple example is shown using Figure b , the velocity-versus-time graph of Figure , to find acceleration graphically. This graph is depicted in Figure a , which is a straight line.The corresponding graph of acceleration versus time is found from the slope of velocity and is shown in Figure b. In this example, the velocity function is a straight line with a constant slope, thus acceleration is a constant.In the next example, the velocity function has a more complicated functional dependence on time. If we know the functional form of velocity, v t , we can calculate instantaneous acceleration a t at any time point in the motion using Figure. A particle is in motion and is accelerating. We find the functional form of acceleration by taking the derivative of the velocity function. Then, we calculate the values of instantaneous velocity and acceleration from the given functions for each.For part d , we need to compare the directions of velocity and acceleration at each time. We see that the maximum velocity occurs when the slope of the velocity function is zero, which is just the zero of the acceleration function. The particle has reduced its velocity and the acceleration vector is negative. The particle is slowing down.The particle is now speeding up again, but in the opposite direction. We can see these results graphically in Figure. Tangent lines are indicated at times 1, 2, and 3 s. The slopes of the tangent lines are the accelerations. Comparing the values of accelerations given by the black dots with the corresponding slopes of the tangent lines slopes of lines through black dots in a , we see they are identical.By doing both a numerical and graphical analysis of velocity and acceleration of the particle, we can learn much about its motion. The numerical analysis complements the graphical analysis in giving a total view of the motion. The zero of the acceleration function corresponds to the maximum of the velocity in this example. Also in this example, when acceleration is positive and in the same direction as velocity, velocity increases.As acceleration tends toward zero, eventually becoming negative, the velocity reaches a maximum, after which it starts decreasing. If we wait long enough, velocity also becomes negative, indicating a reversal of direction. A real-world example of this type of motion is a car with a velocity that is increasing to a maximum, after which it starts slowing down, comes to a stop, then reverses direction. If we take east to be positive, then the airplane has negative acceleration because it is accelerating toward the west.It is also decelerating; its acceleration is opposite in direction to its velocity. You are probably used to experiencing acceleration when you step into an elevator, or step on the gas pedal in your car.Figure presents the acceleration of various objects. We can see the magnitudes of the accelerations extend over many orders of magnitude. In this table, we see that typical accelerations vary widely with different objects and have nothing to do with object size or how massive it is. Acceleration can also vary widely with time during the motion of an object.A drag racer has a large acceleration just after its start, but then it tapers off as the vehicle reaches a constant velocity. Its average acceleration can be quite different from its instantaneous acceleration at a particular time during its motion. Figure compares graphically average acceleration with instantaneous acceleration for two very different motions.Google Maps can tell you your speed, it has an inbuild speedometer, which is only currently for Android users. What you see on the speedometer of a car is the speed at that instant or moment — the instantaneous speed. One way to find this instantaneous speed is to measure the rate of rotation of the wheels. The speedometer of a car reveals information about the instantaneous speed of your car.It shows your speed at a particular instant in time. On the average, your car was moving with a speed of 25 miles per hour. One way of looking at it is that instantaneous speed gives you more details about your journey, especially when your journey consists of variable speeds. The smaller the time interval in which you measure, the more information you have about your journey.Instantaneous speed is found by taking the absolute value of instantaneous velocity, and it is always positive. Average speed is total distance traveled divided by elapsed time. How do you calculate speed?Since distance and time are positive quantities and speed is obtained by the ratio of these two quantities, speed cannot be negative. The average speed cannot be zero unless the body is stationary over a given interval of time. Average speed is the ratio of the total distance travelled by a body to the total time interval taken to cover that particular distance.Answer: a True. When a body begins to fall freely under gravity, its speed is zero but it has non-zero acceleration of. When a particle moves with a constant speed in the same direction, neither the magnitude nor the direction of velocity changes and so acceleration is zero.Can a particle in one- dimensional motion have zero speed and a non-zero velocity? If speed is zero velocity is also zero. A bode can have acceleration without zero velocity. A5 No , it is not possible in straight line motion of particle having 0 speed and non-zero velocity because when speed is 0 , no distance will be covered by the body and displacement will also be 0 , Hence velocity will also be 0.No, a body can not have its velocity constant, while its speed varies. Rather, it can have its speed constant and its velocity varying. For example in a uniform circular motion. Answer: it is not possible to travel metre because when the displacement is zero then it means no distance cover by it.An object that is accelerating is always changing direction. An object has an instantaneous acceleration, even if the acceleration vector is zero. This can mean a change in the object's speed or direction. Average acceleration is the change of velocity over a period of time. Instantaneous acceleration is the change of velocity over an instance of time. The acceleration due to gravity and uniform circular motion are examples of constant or uniform acceleration.Acceleration - Physics Hypertextbook. Acceleration - The Physics Classroom. Acceleration - Wikipedia. Top-rated books on the Physics of Motion. Click on a button to bookmark or share this page through Twitter, Facebook, email, or other services:. The Web address of this page is: www.Please include it as a link on your website or as a reference in your report, document, or thesis. 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