Answer to Question #90892 in Mechanics | Relativity for Ross Duffy

Question

Good morning is it possible to calculate when a dog stops accelerating with the
Dogs weight in kg
The distance traveled
And the time taken to travel

Answer 1

Hello!

Yes, it is possible. The following expressions may help you. But first, we need to be sure what exactly we want to calculate about the dog.

Consider a dog with mass $m$ which stops, i.e. decelerates. Assume that it had initial velocity $v_i$ (fast) and final velocity $v_f$ (slow, or the final speed is zero when the dog fully stops). Also, assume that the force of friction acting on the dog is $f$. The acceleration (deceleration) will be hence

$$a=\frac{f}{m}.$$

The distance traveled before the stop will be

$$d=\frac{v_f^2-v_i^2}{2a}.$$

The time required for the dog to stop is

$$t=\frac{v_f-v_i}{a}.$$