Determine when the velocity of the particle is zero

[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.

Plot the acceleration vs. time. From your plot, determine when the velocity of the particle is zero.

-ok so if when I plot this line, because acceleration is always positive, wouldn't the line just have a constant positive slope. I know you're supposed to find the area under the curve to get the velocity. But when the velocity equals 0? I don't get how I could find this from my
a vs t graph.

 

[ideasrule]

-ok so if when I plot this line, because acceleration is always positive, wouldn't the line just have a constant positive slope.

Yes.

I know you're supposed to find the area under the curve to get the velocity.

Actually, the area under the curve is the change in velocity, not the velocity itself; that's why the question gives you the initial velocity. So if you want v=0, delta v has to be 6 since -6+6=0. When is the area under the graph 6?

 

[tomcue]

Based on the given information, the velocity of the particle will be zero at a specific time when the acceleration is equal to the negative of the initial velocity. In this case, the initial velocity is -6.0m/s, so the acceleration must be equal to 6.0m/s^2 for the velocity to be zero.

To determine when this occurs, we can set the given acceleration function equal to 6.0m/s^2 and solve for t:

1.0 m/s^2 + (0.25 m/s^3)t = 6.0 m/s^2
(0.25 m/s^3)t = 5.0 m/s^2
t = 20 seconds

Therefore, at 20 seconds, the velocity of the particle will be zero. This can also be confirmed by looking at the a vs t graph. At t = 20 seconds, the acceleration will be 6.0m/s^2, which corresponds to the point where the line crosses the x-axis, indicating zero velocity.

It is important to note that the velocity of the particle may also reach zero at other points on the graph, but at these points, the acceleration will not be equal to 6.0m/s^2. The given information only specifies the initial velocity and acceleration function, so we can only determine the specific time when the velocity is zero based on this information.