# Dynamics Problem: Hockey Puck

1. Jun 17, 2017

### aatari

1. The problem statement, all variables and given/known data
Problem:
During a pond hockey game, a puck accelerates from rest at 5.0 m/s 2over a distance of 80.0 cm. The puck then slides with a constant speed for 4.0 s until it reaches a rough section which causes it to stop in 2.5 s.

a. What is the speed of the object when it reaches the rough section?

2. Relevant equations

a = (v2v1) / Δt.............. (1)
Δd = v1Δt + ½aΔt2 ...........(2)
Δd = (v22 v12) / 2a....... (3)
v
2 = v1 + aΔt................... (4)
v22 = v12 + 2aΔd........... (5)

3. The attempt at a solution
Hi guys, I know how to solve this question but I am having trouble understanding when to use which equation. And I am hoping one you can help me understand when to use what equation.

So for the question above we are asked to find the speed of the puck, which is very easy. The way I understand, we can solve this by either using equation (4) or equation (5). Both these equations will give us the final velocity. However, if I use equation 4 my answer is 20 m/s and if I use equation 5, I get 2.8 m/s. This is a significant difference and I dont understand why this is.

How do I figure out when to use what equation in situation like this?

2. Jun 17, 2017

### Staff: Mentor

How can you use equation (4)? You don't have the time.

3. Jun 17, 2017

### aatari

The puck then slides with a constant speed for 4.0 s. Isn't time 4.0 s before the puck reaches the rough section?

4. Jun 17, 2017

### Staff: Mentor

That time is irrelevant for figuring out the speed.

Realize that there are two (really three!) segments to the motion, each quite different: (a) Constant acceleration as it moves from speed zero to some unknown speed; (b) Constant speed for 4 s until it hits the rough spot; (c) Constant acceleration as it slows down to rest.

To find that cruising speed, you must analyze segment (a). Equation (4) won't help you there.

5. Jun 17, 2017

### aatari

Why and how is it irrelevant though? How can someone who is new to this topic in physics can figure this out?

6. Jun 17, 2017

### Staff: Mentor

The given 4.0 seconds is the time the puck was moving at constant speed. It's not the time it took to accelerate from zero to that speed (which is what equation 4 would require).

You need to learn to recognize different types of motion: constant acceleration versus constant velocity, for one. The secret? Solve as many problems as you can! (That's how you get good.)