difficult differentiation ex
The answers are 6m/s,36and27m/s respectively.
- 1 decade agoFavorite Answer
Given that the displacement of P at time t is s=15t+6t²-t³
Let f(t) be the s at time t,so
As f(0)=0, s=0 when t=0,
the average velocity over the first t seconds equals s/t
Thefore, the average velocity of P over the first 2 seconds is 23m/s
Given that the displacement of P at time t equals s=15t+6t²-t³
From (a), f(t)=s=15t+6t²-t³
When v=0, P comes to instantaneous rest
t=-1 or t=5
As t=-1 is meaningless, P comes to instantaneous rest at t=5
Therefore, when P comes to instantaneous rest,
The value of s when P comes to instantaneous rest is 100
From (a) and (b),
When the acceleration of P is instantaneously zero, a=0
Therefore, the acceleration of P is instantaneously zero at t=2
The velocity of P when its acceleration is instantaneously zero is 27m/s
- wyLv 71 decade ago
Since s=15t +6t^2 -t^3.
Therefore, ds/dt= speed = 15 +12t -3t^2.
when t=0, ds/dt=15, when t=2, ds/dt=27. herefore, average speed for the first 2 sec.=(15 +27)/2=42/2=21.
When ds/dt=0, that is 15+12t-3t^2=0, t=5 or -1(reject). Therefore, at t=5,
s= 15 x5 + 6 x 5 x 5 - 5 x5 x5 =100.
Since speed, v=15 +12t -3t^2, therefore, accelaration=dv/dt=12 -6t=a.
When a=0, t=2, therefore, v=15 + 12 x2 - 3 x2 x2=27.
- hawk_wing_1999Lv 61 decade ago
t=0, v=15, t=1, v=24, t=2, v=27
(b)When P comes to instantanteous rest, v=0
t=5 or -1(rej.)
Value of s when t=5 is 75+150-125=100metres
Value of s what t=2 is 30+24-8=46metres