Dynamics in Motion: Solving Problems with Acceleration and Velocity Equations

[aatari]

Homework Statement

Problem: [/B]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?

Homework Equations

[/B]
a = (v₂ − v₁) / Δt..... (1)
Δd = v₁Δt + ½aΔt² ...(2)
Δd = (v₂² − v₁²) / 2a... (3)
v₂ = v₁ + aΔt...... (4)
v₂² = v₁² + 2aΔd... (5)

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 don't understand why this is.

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

 

[Doc Al]

The way I understand, we can solve this by either using equation (4) or equation (5).

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

 

[aatari]

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

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?

 

[Doc Al]

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?

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.

 

[aatari]

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.

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

 

[Doc Al]

Why and how is it irrelevant though?

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).

How can someone who is new to this topic in physics can figure this out?

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.)