Velocity, Time, and Distance Problem

[adds17]

Homework Statement

A bunny runs along a straight path at a constant velocity of 25 m/s [N] when it passes a sleeping groundhog who immediately beings to chase the bunny with a constant acceleration of 3.0 x 10^-3 m/s^2. How long before the bunny is caught by the groundhog? How far would the groundhog go before catching the bunny? what would be the groundhog's final speed? Is this reasonable?

Homework Equations

d=vt

d=at^2/2

Since they both equal d, they equal each other.

vt=at^2/2

The Attempt at a Solution

I plugged in the numbers and came up with an answer of 16666.6 s. (Roughly 4 hrs 37 min)
I'm just not sure if I'm doing this correctly...any tips or advice?

 

[Pengwuino]

Yup that's how to do that part of the problem. Notice the acceleration is amazingly slow and that is why it is going to take so long to catch up. With the time you can simply plug into solve the rest of the problem.

 

[nlightner]

As a scientist, it is important to always double check your calculations and equations to ensure accuracy. In this problem, you correctly used the equations d=vt and d=at^2/2, and then set them equal to each other to solve for time. Your answer of 16666.6 s seems reasonable based on the given information and equations used.

To further verify your answer, you could also use the equation v = u + at (where u is initial velocity) to calculate the final velocity of the groundhog. If the final velocity is close to 25 m/s, then your answer for time is likely correct.

To find the distance traveled by the groundhog, you can plug in the calculated time into the equation d=vt. This will give you the distance in meters.

In terms of reasonableness, it is important to consider the physical limitations of the bunny and groundhog. Can the groundhog realistically accelerate at a constant rate of 3.0 x 10^-3 m/s^2 for a long period of time? Are there any external factors, such as obstacles or terrain, that could affect the chase? These are important factors to consider when evaluating the reasonableness of the problem.