A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1
Answer:
Velocity = 131 m/s
Speed = 131 m/s
Explanation:
Equation of motion, s = f(t) = 12t² + 35 t + 1
To get velocity of the particle, let us find the first derivative of s
v (t) = ds/dt = 24t + 35
At t = 4
v(4) = 24(4) + 35
v(4) = 131 m/s
Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s
Silver is a very good conductor, this means its resistivity is very low (from table, we can check the precise value, which is

).
Pure water, instead, is a very bad conductor, this means its resistivity is very high, of order of

(

). Even without knowing the precise value of the pure water resistivity, we can estimate the ratio between the pure water resistivity and the silver resistivity by comparing the two orders of magnitude:

Therefore, we can say that the correct answer is
Answer:
BC and DE
Explanation:
In the given figure, the velocity time graph is shown. We know that the area under v-t curve gives the displacement of the particle.
Area under AB, 
Area under BC, 
Area under CD, 
Area under DE, 
Area under EF, 
So, form above calculations it is clear that, during BC and DE undergo equal displacement. Hence, the correct option is (c) "BC and DE = 4 meters".
Answer:
Speed will be equal to 1.40 m/sec
Explanation:
Mass of the rubber ball m = 5.24 kg = 0.00524 kg
Spring is compressed by 5.01 cm
So x = 5.01 cm = 0.0501 m
Spring constant k = 8.08 N/m
Frictional force f = 0.031 N
Distance moved by ball d = 15.8 cm = 0.158 m
Energy gained by spring

Energy lost due to friction

So remained energy to move the ball = 0.0101 - 0.0048 = 0.0052 J
This energy will be kinetic energy


v = 1.40 m/sec
Answer:
The inducerd emf is 1.08 V
Solution:
As per the question:
Altitude of the satellite, H = 400 km
Length of the antenna, l = 1.76 m
Magnetic field, B = 
Now,
When a conducting rod moves in a uniform magnetic field linearly with velocity, v, then the potential difference due to its motion is given by:

Here, velocity v is perpendicular to the rod
Thus
e = lvB (1)
For the orbital velocity of the satellite at an altitude, H:

where
G = Gravitational constant
= mass of earth
= radius of earth

Using this value value in eqn (1):
