## Ruchi. 3 years ago 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.

1. apoorvk

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

2. apoorvk

wrt 'time' ofcourse.

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

4. yakeyglee

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.

v=dx/dt

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

7. Ruchi.

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

8. Ruchi.

am i right.

Yeah, perfect @Ruchi.

So, we get|dw:1338103103383:dw|

12. yakeyglee

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

13. Ruchi.

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

Acceleration is not uniform

21. apoorvk

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

22. yakeyglee

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

23. him1618

Bt that isnt in the domain@ yakeyglee

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

25. apoorvk

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

When the accn is not a function of time

27. apoorvk

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

28. him1618

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

velocity is dx/dt

32. yakeyglee

@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

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

35. him1618

c=4

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

37. him1618

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