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
Answer: The acceleration of the object is 0.67m/s^2 west.
Explanation: Here we are given the initial velocity and final velocity as well as the time taken. Acceleration is the change in velocity per unit time, thus the equation becomes.
a=dv/t
a=vf-vi/t
a=-2.1-4.7/3.9
a= 0.66m/s^2 west
Answer:
Explanation:
Intensity of light is inversely proportional to distance from source
I ∝ 1 /r² where I is intensity and r is distance from source . If I₁ and I₂ be intensity at distance r₁ and r₂ .
I₁ /I₂ = r₂² /r₁²
If r₂ = 4r₁ ( given )
I₁ / I₂ = (4r₁ )² / r₁²
= 16 r₁² / r₁²
I₁ / I₂ = 16
I₂ = I₁ / 16
So intensity will become 16 times less bright .
"16 times " is the answer .
Answer:
We have to show surface area
,with few conditions that is by considering Force
and Pressure
to be respectively.
Explanation:
The atmospheric pressure is
on Earth's surface.
The magnitude of the force exerted on a person by the atmosphere is
.
Now to calculate surface area we can find it from
and re-arranging it to.

So plugging the values,
Surface area 
Hence from the above calculations we can say that surface area is
.
So the surface area of an average person can be said to have
, using the concept of pressure and force.