A) We differentiate the expression for velocity to obtain an expression for acceleration:
v(t) = 1 - sin(2πt)
dv/dt = -2πcos(2πt)
a = -2πcos(2πt)
b) Any value of t can be plugged in as long as it is greater than or equal to 0.
c) we integrate the expression of velocity to find an expression for displacement:
∫v(t) dt = ∫ 1 - sin(2πt) dt
x(t) = t + cos(2πt)/2π + c
x(0) = 0
0 = = + cos(0)/2π + c
c = -1/2π
x(t) = t + cos(2πt)/2π -1/2π
Answer:
Explanation:
Force, F = - mg j
r = - 7x i + y j
Torque is defined as the product f force and the perpendicular distance.
It is also defined as the cross product of force vector and the displacement vector.


[tex]\overrightarrow{\tau }= 7 m g x k
Here, we observe that the torque is independent of y coordinate.
Answer:
Explanation:
Given
Distance = 4.0m
Time = 5.0 mins = 300secs
Required
Average speed
Average speed = Distance/Time
Average speed = 4.0/300
Average speed = 0.01333m/secs
Hence the average speed of the snail is 0.01333m/s
Answer:
k = 2.279
Explanation:
Given:
Magnitude of charge on each plate, Q = 172 μC
Now,
the capacitance, C of a capacitor is given as:
C = Q/V
where,
V is the potential difference
Thus, the capacitance due to the charge of 172 μC will be
C = 
Now, when the when the additional charge is accumulated
the capacitance (C') will be
C' = 
or
C' = 
now the dielectric constant (k) is given as:

substituting the values, we get

or
k = 2.279