Position And Velocity Vs. Time

Classical Mechanics Level 1

Consider a particle which starts from rest and has position $x(t) = t^2$ . What is the color of the curve which represents its velocity as a function of time?

Different possible graphs of velocity vs time.

Blue Gold Green Red

1 solution

Sravanth C.
Apr 13, 2016

Observe that the velocity of an object is the derivative of it's displacement function. Thus, in this case, as the displacement function is modelled by $x(t)=t^2$ , the velocity would be given by:

$\begin{aligned} v(t)&=\dfrac{d}{dt}x(t)\\ &=\dfrac{d}{dt}x^2\\ &=2t \end{aligned}$

Clearly the only graph which is satisfying the function: $v(t)=2t$ is the $\color{#D61F06}{\text{red line}}$ .

Correct me if I'm wrong. But I didn't use any math, just looked at the graphs and realised that if something start from rest (0 m/s) it has to cross where X and T "crossing" in this graph, which must be 0 Therfore it had to be the red one.

Apologies for some bad English grammatical and word choices.

Hannes Camitz - 5 years, 2 months ago

Hmm... in this case it might help but it's not the actual way to do it, even if it is correct why won't the green one satisfy your reasoning?

Sravanth C. - 5 years, 2 months ago

Good point. I'm sorry but when you put that way I realised that it was luck and I can't give you a proper answer nor reasoning.

Hannes Camitz - 5 years, 2 months ago

@Hannes Camitz – Haha, never mind. Hope my solution gives you a better insight to the problem. Thanks! $\ddot\smile$

Sravanth C. - 5 years, 2 months ago

Position And Velocity Vs. Time

1 solution

0 pending reports