Evaluate a Particle's Position at Given Times

[AryRezvani]

Homework Statement

The position of a particle moving along the x-axis varies in time according to the expression x = 3t 2, where x is in meters and t is in seconds. Evaluate its position at the following times.
(
a) t = 2.30 s


(b) t = 2.30 s + Δt


(c) Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.30 s.
m/s

Homework Equations

Listed above.

The Attempt at a Solution

Well for part 'a)', I plugged in the given time (2.30) and got 15.87 meters.

At part 'b)' is where I get stumped. What would you do to find delta t?

Thanks.

 

[gneill]

Homework Statement

The position of a particle moving along the x-axis varies in time according to the expression x = 3t 2, where x is in meters and t is in seconds. Evaluate its position at the following times.
(
a) t = 2.30 s


(b) t = 2.30 s + Δt


(c) Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.30 s.
m/s

Homework Equations

Listed above.

The Attempt at a Solution

Well for part 'a)', I plugged in the given time (2.30) and got 15.87 meters.

At part 'b)' is where I get stumped. What would you do to find delta t?

Thanks.

You don't find Δt; You plug in the symbol Δt and expand the expression; at this point it is simply a variable. It may be worthwhile to replace the initial value of t (2.30s) with a symbol, too. Say, t_o = 2.30s. This may help keep the subsequent manipulations neat.

For part (c) you need to understand what is meant by Δx. That is, the change in x.

 

[AryRezvani]

You don't find Δt; You plug in the symbol Δt and expand the expression; at this point it is simply a variable. It may be worthwhile to replace the initial value of t (2.30s) with a symbol, too. Say, t_o = 2.30s. This may help keep the subsequent manipulations neat.

For part (c) you need to understand what is meant by Δx. That is, the change in x.

Okay, so all you do is plug in the variables.

So I came up with X = 3(T+TΔ)^2

Would I FOIL it out, or something? How do I come up with a numerical answer?

 

[AryRezvani]

I just foiled and got 3(5.29 + 4.60ΔT + ΔT^2)

Stuck here now, shoot. I have a feeling I'm way off...

 

[gneill]

Okay, so all you do is plug in the variables.

So I came up with X = 3(T+TΔ)^2

Would I FOIL it out, or something? How do I come up with a numerical answer?

You don't. There's no numerical answer to this part unless a specific Δt is provided. A symbolic result is sometimes what you're looking for. Move on to the next part.