Confused whether an object is at rest or has velocity at t=0

[Indigo_Blue]

Homework Statement

So i have this lab where I am supposed to push a car up an inclined ramp. I record the time it takes for the object to reachest the highest point on the inclined ramp before it goes back down. I am supposed to create a position vs time graph, velocity vs time graph, and acceleration vs time graph.

Then I have to use the equations for constant acceleration in order to find velocity, acceleration, and distance at certain points.

Homework Equations

The Attempt at a Solution

I understand how to use the equations to find the unknown variables, but I cannot conceptualize what the initial velocity of the object would be especially when time=0. I don't know if the velocity is 0 since the object was a rest before I pushed it or if I am instead supposed to use the positive velocity right after the moment I pushed the object. So if I make a velocity vs time graph from the position vs time graph that is a parabola concaving down, what is the velocity of the object at t=0. Is it at rest or there is supposed to be a velocity at time=0. I don't understand how I can even find the velocity at t=0. How can I use a tangent line when t=0?
I am also supposed to find the constant acceleration but I'm not even sure what my initial velocity is.

 

[Chandra Prayaga]

Let us look at the problem in steps.
1. Is the car all the time on the inclined plane or is it being pushed so fast that it reaches the end of the inclined plane and jumps off.?
2. What does the velocity vs time graph look like?
3. Does the problem ask you to solve for something "after you push it", "before you push it", or "while you are pushing it"? In each case, the velocities and acceleration are different.

 

[gneill]

I understand how to use the equations to find the unknown variables, but I cannot conceptualize what the initial velocity of the object would be especially when time=0. I don't know if the velocity is 0 since the object was a rest before I pushed it or if I am instead supposed to use the positive velocity right after the moment I pushed the object.

Most likely the initial velocity would be taken to be the moment that you stopped pushing the car. That would be your t = 0 instant, too. If you have measured data to follow the time during which you were pushing the car, then the answer might be different. If you're pushing the car manually, it would be difficult to predict the actual force applied (and hence the acceleration) over time.

Perhaps you could post the text of the lab directions so that we can offer precise suggestions.

 

[Indigo_Blue]

Let us look at the problem in steps.
1. Is the car all the time on the inclined plane or is it being pushed so fast that it reaches the end of the inclined plane and jumps off.?
2. What does the velocity vs time graph look like?
3. Does the problem ask you to solve for something "after you push it", "before you push it", or "while you are pushing it"? In each case, the velocities and acceleration are different.

1.The car is given a slight push. It goes up the ramp, then it slides back down to its initial position.
2. I don't really know the velocity time graph, but the position vs time graph is a parabola that concaves down. I think I am supposed to draw a tangent line on the position vs time graph to get the initial velocity, but I am not sure how to do it.
3. There isn't a question. We just have to graph the motion of the car.

 

[CWatters]

All that looks reasonable.

 

[CWatters]

I understand how to use the equations to find the unknown variables, but I cannot conceptualize what the initial velocity of the object would be especially when time=0. I don't know if the velocity is 0 since the object was a rest before I pushed it or if I am instead supposed to use the positive velocity right after the moment I pushed the object.

Could do both. Since time ticks along at a constant rate you could break the motion down into several phases and analyse each phase on its own, setting t=0 at the start of each phase.

I would start by looking at what happens after you have let go of the car. It will start with some initial velocity U that you have given it and decelerate as it goes up the ramp. You can apply the equations of motion to each phase or a combination of phases (eg going up and down can be analysed has two separate phases or just one). You can calculate the initial velocity by drawing the tangent as you suggested.

Then when that's all done you can think about what happened _while_ you were pushing it. Most likely it started from rest. It ended up with velocity U. Perhaps you could assume you applied a constant force to accelerate it from one to the other in between. Sketch a possible graph. State any assumptions made and add some comments such as "I have assumed constant acceleration in this phase but it might not have been constant, in which case the line would be ... rather than ..."

Plot or sketch a graph for each phase separately then join them together on one final combined graph. You can choose where t=0 goes on the final graph by moving the whole graph left or right. It could be at the point where you start pushing, or the point where you let go, your birthday or the start of the universe (Although if you pick the start of the universe as t=0 you would need a big sheet of paper to fit it all on and not much would happen until the end :-) The point is that the duration of each phase doesn't depend on where you set t=0. If it takes 4 seconds to go up the ramp it will still take 4 seconds regardless of where you define t=0.

 

[CWatters]

PS You can find the velocity at any point on a graph of position by drawing the tangent to the curve at that point.