## Ruchi. Group Title displacement time equation of a particle moving along x-axis is x=20+t3-12t. a)find velocity of particle at time t=0 b)state whether the motion is uniformly acceleration or nt. c)find position of the particle when v=0. 2 years ago 2 years ago

1. apoorvk Group Title

if that^ is the equation of the displacement, how would you get the equation for velocity?

2. apoorvk Group Title

wrt 'time' ofcourse.

"Substitute" the value of "t" and find.

4. yakeyglee Group Title

Hint for part (a): $$v=\frac{dx}{dt}$$ Hint for part (b): $$a=\frac{dv}{dt} = \frac{d^2x}{dt^2}$$. If this is a function of time, then it is not constant. Hint for part (c): What $$t$$ values satisfies this condition?

5. Ruchi. Group Title

v=dx/dt

Sorry. @yakeyglee is absolutely correct. Follow his steps and ur answer is done

7. Ruchi. Group Title

as v=0,we 0=3t2-12

8. Ruchi. Group Title

am i right.

Yeah, perfect @Ruchi.

So, we get|dw:1338103103383:dw|

12. yakeyglee Group Title

More specifically, $$t=\pm 2$$.

13. Ruchi. Group Title

a)=-12m/s

But, "t" cannot be negative, so t = 2. so, c) 2

A) -12m/s correct. sorry for my error.

On double differentiation, we get, a = 6t (I think I am correct).

So, unifrom acceleration

19. him1618 Group Title

Acceleration is not uniform

21. apoorvk Group Title

No as a=6t, acceleration is dependent on time. So it's not uniform.

22. yakeyglee Group Title

$$t$$ most certainly can be negative. It simply corresponds to be fore $$t=0$$.

23. him1618 Group Title

Bt that isnt in the domain@ yakeyglee

So @apoorvk bhai, when can we say that a is uniform? in what relation?

25. apoorvk Group Title

And put in the value of 't' when v=0 from the first part, in the equation of displacement, that is put in t=2. That should give you the displacement at the time when v=0.

26. him1618 Group Title

When the accn is not a function of time

27. apoorvk Group Title

uniform means constant - it isn't constant is it?

28. him1618 Group Title

In this case accn is a function of time...so its not uniform

Thanks all, I understood.

But, plz show me what will be the answer of (a), (b) and (c)

31. him1618 Group Title

velocity is dx/dt

32. yakeyglee Group Title

@him1618 I don't see any statement of the domain...it's usually assumed $$t\in\mathbb R$$, which includes negative values.

So, (a) = -12, (c) = 2, (b) = not uniform. Is this the final answer? Please say.

34. him1618 Group Title

it is so my man..bt not here..this is simple/...were not into time domain circuits here :P

35. him1618 Group Title

c=4

Is (a) and (b) what i gave the answer rite? How is (c) = 4?????????

37. him1618 Group Title

v=0 means 3t^2 - 12 =0 t=2 Put t=2 in x(t)