Question

Objects that move in a straight line with a constant speed—not speeding up or slowing down—have zero acceleration. We call this kind of motion: Uniform Motion. We can identify uniform motion when the object travels equal distance intervals in equal times.

We can identify non-uniform motion, or accelerated motion, when the object travels equal distance intervals in unequal times. Finally, we have two types of non-uniform motion: motion with constant acceleration and motion with a non-constant (or changing) acceleration.

Activity 1

Today you will analyze the motion of a cart traveling along an inclined track. You will begin by doing a thought experiment, predicting the motion of your object. Discuss your ideas among your group…it is okay to disagree!

Sketch an acceleration-versus-time graph for an object, starting with some initial speed, traveling on a flat track. Remember, this sketch is a prediction; what do you think it would look like? Then sketch a velocity-versus-time graph for the same case.

1. Explain the shape of your acceleration graph.

2. Explain the shape of your velocity graph

Sketch an acceleration-versus-time graph and a velocity-versus-time graph for an object, starting with some initial speed, traveling down an inclined track.

3. Explain the shape of your acceleration graph.

4. Explain the shape of your velocity graph

Activity 2

Now, using a track, cart meter stick and stopwatches, you will make some measurements to determine if a cart traveling down a ramp follows uniform or non-uniform motion.

First, mark a start point and end point on your track that is at least 1.5m long.

5. How many time/distance data points, between start and end, will be necessary to determine whether the cart is traveling with uniform or non-uniform motion? Explain your choice. Note: you may want to look at Questions 8 & 9 to help inform your choice.

6. Now, outline your measurement plan (procedure) to make this determination of uniform or non-uniform motion. You procedure should include clear instructions, such that anyone could reproduce you experiment exactly.

7. Create a data table and record your data in the space below.

8. Now you will need to use your data to calculate velocities and accelerations. Recall that we have discussed average velocity as vavg = Δx/Δt as well as vavg = (vi + vf)/2. We also discussed average acceleration as aavg = Δv/Δt. Using these equations, calculate the instantaneous velocity of your cart at each distance/time data point and the average acceleration between each pair of distance/time data points. When you have completed your calculations, organize your results into a table with four columns: time, position, velocity, and average acceleration.

9. Now you will graph your results. Plotting [1] a graph of position (y-axis) vs. time (x-axis); [2] a graph of velocity (y-axis) vs. time (x-axis); and [3] a graph of acceleration (y-axis) vs. time (x-axis). Be sure to fully label your graphs. This may be done on a computer or on graph paper. Attach your graphs to the back of this packet.

10. Based on your data and results, answer the lab questions: does a cart traveling down a ramp follow uniform or non-uniform motion? If it follows non-uniform motion, is the acceleration constant or non-constant? Support your answer with evidence from your experiment.

11. Are you confident in your answer to question 10? Explain why or why not.

12. Now, compare your answer (and resulting graphs) to the prediction sketches you made in Activity 1. Do your predictions match your results? If not, which do you believe (prediction or results) and why?

13. Finally, take some time to evaluate your procedure. Do you think it was an effective procedure? Were there any problems with it? How would you change/improve upon the procedure if you were to repeat this experiment?

trial 1	trial 2	trial 3	trial 4	trial 5
2.7s	2.45s	2.9s	2.58s	2.82s

Answer 1

Q. Sketch an acceleration-versus-time graph for an object, starting with some initial speed, traveling on a flat track.

Example of Uniform motion of an object.

Let an object moving on a flat track with initial velocity . If there is no any external force applying on the object then according to Newton's first law the body will remains in motion throughout the

Following graph shows the distance traveled by the the object as the time elapse

By considering kinematic equation for an object moving in straight line,

As there is no external force on the body by the equation

Therefore equation of motion becomes

..................................................................................................................(1)

This equation is similar to equation of straight line having some slope passing through origin

Velocity Vs time graph

From the assumption velocity of the object is constant throughout the motion or

Velocity is the rate of change of position with respect to time

From equation (1)

..................................................................................................................(2)

Graph shows that the object moves with constant velocity throughout the motion.

Acceleration Vs time graph

As discussed earlier, there is no external force acting on the object so acceleration is zero or

Acceleration is the rate of change of velocity with respect to time

From equation (2)

The acceleration of the object is zero throughout the motion.

Following is the acceleration vs time graph

Graph shows that acceleration of the object is zero throughout the motion.

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Q.Sketch an acceleration-versus-time graph and a velocity-versus-time graph for an object, starting with some initial speed, traveling down an inclined track.

Example of non-uniform motion of an object

Let us suppose a ball is rolling down on an inclined plane making angle with the horizontal. Neglecting frictional force and rotational motion of the ball, the only force acting on the ball is gravitational force straight downward as shown in figure.

Resolving the components of the gravitational force along x and y axis

The forces acting on a ball along y axis

As there is no motion of the ball along y direction, sum of all forces acting along y axis must be zero

Thus the acceleration of the body moving inclined track is . As g and are constant value of a remains constant throughout the motion.

Let initial velocity of the ball be

Using equation of motion for object moving in straight line with constant acceleration

................................................................................................(3)

Velocity Vs time graph

Velocity is the rate of change of position with respect to time

From equation (3)

.....................................................................................................................(4)

Plotting the above equation gives us shape of the Velocity vs time graph, shown below

The graph shows that as the time elapsed the velocity of the ball goes on increasing from initial velocity to

Acceleration Vs time graph

Acceleration is the rate of change of velocity with respect to time

From the equation (4)

Plotting the above equation gives us the shape of the acceleration vs time graph. Which is having straight line nature having constant slope a'.

At t=0 there is no change of velocity so at t=0 a'=0, and as time elapse the ball moves with constant acceleration