## anonymous 4 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. anonymous

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

2. anonymous

wrt 'time' ofcourse.

3. anonymous

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

4. anonymous

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. anonymous

v=dx/dt

6. anonymous

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

7. anonymous

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

8. anonymous

am i right.

9. anonymous

Yeah, perfect @Ruchi.

10. anonymous

So, we get|dw:1338103103383:dw|

11. anonymous

12. anonymous

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

13. anonymous

a)=-12m/s

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

So, unifrom acceleration

18. anonymous

19. anonymous

Acceleration is not uniform

20. anonymous

21. anonymous

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

22. anonymous

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

23. anonymous

Bt that isnt in the domain@ yakeyglee

24. anonymous

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

25. anonymous

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. anonymous

When the accn is not a function of time

27. anonymous

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

28. anonymous

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

29. anonymous

Thanks all, I understood.

30. anonymous

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

31. anonymous

velocity is dx/dt

32. anonymous

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

33. anonymous

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

34. anonymous

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

35. anonymous

c=4

36. anonymous

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

37. anonymous

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

38. anonymous

Still bhaiya, we get, 20 + 2*3 - 12*2 = 2. Am I rite????????