Answer:
Step-by-step explanation:
The position of an object moving horizontally after t seconds is given by the function
s = 3t - t³
a) The object is stationary when there is no external force acting on the body. When the body is at rest, the body remains in a position and here is no distance covered by the object i.e s = 0
b) velocity is the change in displacement of a body with respect to time.
v = ds/dt
S = 3t - t³
V = ds/dt = 3-3t²
at t = 2
Velocity = 3-3(2)²
Velocity = 3-12
Velocity = -9m/s
c) acceleration is the change in velocity of a body with respect to time.
acceleration = dv/dt
If v = 3-3t²
a = dv/dt = -6t
When v = 0
0 = 3-3t²
-3 = -3t²
t² = 1
t = ±√1
t = 1sec
The acceleration of the object at v = 0 occurs at t = 1sec and -1sec
a = -6(1)
a = -6m/s²
d) Given the speed of the body v modelled by the function
v = 3-3t²
The speed is decreasing when it is less than zero as shown:
3-3t²< 0
3<3t²
1<t²
±1<t
1<t and -1<t
t>±1
t >1 and t>-1
The speed is decreasing when
3-3t²<0 and t>1 or t>-1
The relation is a function
Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(1, 0, −1), Q(3, 3, 0), R(3, −3, 0), S(1, −2, 2)
topjm [15]
Answer:
the volume of the parallelepiped is = 36
Step-by-step explanation:
given,
P(1, 0, −1), Q(3, 3, 0), R(3, −3, 0), S(1, −2, 2)
PQ = Q - P = (2, 3, 1)
PR = R - P = (2, -3 , 1)
PS = S - P = (0, -2 , 3)
now volume of parallelopiped
[PQ PR PS] = 
now calculating determinant of the matrix
= 2 (-9+2) - 3 (6-0) + 1 (-4-0)
= -14 - 18 - 4
= -36
hence , the volume of the parallelepiped is = 36
