Solve for Position: Physics Question with Initial Position and Velocity

[you_of_eh]

A particle has an initial position X=0m and an initial velocity v=-6.0m/s. Its acceleration is given by the function [1.0 m/s^2 + (0.25 m/s^3)t] where t is in seconds.

Use calculus to find the position of the particle at the instant when its velocity is zero.


-this is a bonus question on an assignment..its a bonus because we haven't started calculus yet, therefore I have no idea how to do it.

Thanks

 

[Pengwuino]

If you don't know any calculus, you can't really do it... unless you do it graphically and knew what the geometric idea behind integration is without really having to know what integration is.

 

[tomcue]

for your question! Calculus is an important tool in solving physics problems, so it's great that you are already thinking about it even before starting your class. Let me walk you through the steps to solve this problem.

First, we need to understand what the question is asking. It is asking for the position of the particle at the instant when its velocity is zero. This means that we need to find the time when the velocity is zero, and then use that time to find the position.

To find the time when the velocity is zero, we can set the acceleration function equal to zero and solve for t. So, we have:

1.0 m/s^2 + (0.25 m/s^3)t = 0

Solving for t, we get t = -4 seconds. This means that at 4 seconds, the velocity of the particle is zero.

Now, to find the position at this instant, we can use the position function, which is given by:

x(t) = x0 + v0t + (1/2)at^2

Where x0 is the initial position, v0 is the initial velocity, and a is the acceleration.

Plugging in the values we have, we get:

x(4 seconds) = 0m + (-6.0m/s)(4 seconds) + (1/2)(1.0 m/s^2 + (0.25 m/s^3)(4 seconds)^2

= -24m + (1/2)(1.0 m/s^2 + 4.0 m/s^2)

= -24m + 2.5m

= -21.5m

Therefore, the position of the particle at the instant when its velocity is zero is -21.5m.

I hope this helps! Keep practicing and don't be afraid to ask for help when needed. Good luck with your studies.