Solve Mechanics Questions: Velocity, Position & Frictionless Plane

[Homophome]

Hi, this is my first post. My teacher gave us some very "hard" homework questions:
Alright: The first question concerns a car moving with acceleration 5t^{2} and initial velocity 4 m/s.

a) what is it's velicity at time t?

b) what is it's position at time t?

c) How far has it gone after time t=pi seconds.

2)

a) Assume I have a frictionless plane inclined at pi/2 radians and a box 6 ft up the plane, how long does it take to fall?

b) Assuming the rock took ten seconds to fall, how high did it start up?

 

[inverseint]

Hey!

I remember doing homework with questions like these!

1.
a) Remember, an object's velocity is simply the integral of its accelleration.
So, the integral of 5t^2 is 5/3t^3 + c.
v=5/3t^3 + c.

b) Like the first question, the objects position at time t is the integral of its
velocity, so the position of the object is 5/12t^4 + t + initial position.
d=5/12t^4+t+c.

c) Just use pi in place of t in the position equation.
d=5/12pi^4+pi+c.2.
a) Since a 'ramp' at pi/2 radians is vertical, you can calculate how long the rock
takes to fall using the accelleration of gravity=9.8 m/s^2.
6 = 1/2 * 9.8 * t^2
12 = 9.8 * t^2
12/9.8 = t^2
t = (12/8.8)^1/2 s.

b) height = 1/2 * 9.8 * 10^2
height = 2 * 9.8 * 100
height = 1960 m.

I hope that helps!

 

[Homophome]

Your first answer isn't what it says in my teachers manual... But thanks anyways.

 

[inverseint]

Oh crap! Your right, I forgot the +c. Editing to fix it...

 

[Homophome]

Thanks a lot, I don't trust this manual anyways.

 

[inverseint]

Thanks a lot, I don't trust this manual anyways.

Haha, yeah, you have to think for yourself sometimes!
No problem.

 

[Homophome]

Edit: Your asnwers don't work... sorry. : (. Also, webassign requires me to graph position vs. time, could you draw me a graph?

 

[inverseint]

Edit: Your asnwers don't work... sorry. : (. Also, webassign requires me to graph position vs. time, could you draw me a graph?

What? I thought they were right. Maybe double check your variables and that you are typing things in right?
I'm not going to draw a graph, but for the second one with the falling rock, it will look like a decreasing quadratic function. Check my attached graph (not exact... ms paint lol!) for what it may look like if you zoom into the right spot. It will be a decreasing parabala centered on the x=zero.

 

[Homophome]

Where are the units on that graph? It looks like a kid drew that! Not helpful at all. Can someone please help me?!??!