Mechanics Problem: Plot the path for s(t)=At-Bt^2+Ct^3

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prehisto
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Homework Statement


hi,guys!
Problem:
s(t)=At-Bt^2+Ct^3,where A,B,C is know constants.
What is the path,velocity and accelartion after 2s from beginning of motion.

Homework Equations



The Attempt at a Solution


So
v(t)=s'(t)
a(t)=s''(t)

But where i get confuzed is when I am asked to calculate v,s,a after 2s.
If i would calculate s(t=2s),v(t=2s),a(t=2s) it would be at time 2s not after 2s,am i right? so how to calculate after 2s?
 

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Imagine that you start the stopwatch at the instant the motion starts. The time t is the reading on the stopwatch. When 2 s elapsed after the start, the reading is 2 s. Just substitute t= 2s.

ehild
 
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prehisto said:

Homework Statement


hi,guys!
Problem:
s(t)=At-Bt^2+Ct^3,where A,B,C is know constants.
What is the path,velocity and accelartion after 2s from beginning of motion.

Homework Equations



The Attempt at a Solution


So
v(t)=s'(t)
a(t)=s''(t)

But where i get confuzed is when I am asked to calculate v,s,a after 2s.
If i would calculate s(t=2s),v(t=2s),a(t=2s) it would be at time 2s not after 2s,am i right? so how to calculate after 2s?
This is semantics. They meant "at" 2 s.
 
15866375797331091037070.jpg

But I can't find the path of the body.Do you know?
 
The "path" is the location of the object at any time. This is what is described by s(t), which is the position at time t.

Zz.
 
Isn't path supposed to be the trajectory of the body?S(t) represents the instantaneous position of the body.
 
Rongeet Banerjee said:
Isn't path supposed to be the trajectory of the body?S(t) represents the instantaneous position of the body.

But what's the difference? You are only given s(t), not x(t), y(t), and z(t) so that you can plot out the "path" in 3D.

Look carefully at the question. The mentioning of the "path" is followed by "velocity" and "acceleration", which all came out of s(t). So s(t) is what the question is asking for from my perspective.

Zz.
 
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Oh I got it
☺️👍.Thank You
 

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ZapperZ said:
The "path" is the location of the object at any time. This is what is described by s(t), which is the position at time t.

Zz.
Yes, the path is s as a function of t, but the question asks for the path at 2 seconds, which makes no sense. It must mean position.
 
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Oh right.I have actually found the position.