Answer:
a) 10m
b)
i)
ii)
iii)
Explanation:
The first 2.0s the sprinter maintains a constant acceleration. So we have to use the Constant acceleration motion formulas to solve the first part of the movement, then we need to use the contant velocity motion formulas for the rest of the movement.
a)
b)
the sprinter run 10 meters with constant accelaration then it start a constant velocity movement, so:
i) x=50-10=40m
ii) x=100-10=90m
iii) x=200-10=190m
Answer:
145.8 cm³ of paint
Explanation:
d₁ = Smaller diameter paintball = 5 cm
d₂ = Larger diameter paintball = 9 cm
V₂ = Volume of larger diameter paintball
Volume of smaller diameter paintball
Similarly
Dividing the above two equations, we get
∴ The larger one hold 163.296 cm³ of paint
If gravitational effects from other objects are negligible, the speed of the rock at a very great distance from the planet will approach a value of
<u>Explanation:</u>
To express velocity which is too far from the planet and escape velocity by using the energy conservation, we get
Rock’s initial velocity
, . Here the radius is R, so find the escape velocity as follows,
Where, M = Planet’s mass and G = constant.
From given conditions,
Surface potential energy can be expressed as,
R tend to infinity when far away from the planet, so
Then, kinetic energy at initial would be,
Similarly, kinetic energy at final would be,
Here,
Now, adding potential and kinetic energies of initial and final and equating as below, find the final velocity as
'm' and as common on both sides, so gets cancelled, we get as
We know, , it can be wriiten as
, we get
Taking squares out, we get,
Answer:
Explanation:
Given that:
For a first order instrument with a sensitivity of .4 mV/K
constant c = 25 ms = 25 × 10⁻³ s
The initial temperature = 273 K
The final temperature = 473 K
The initial volume = 0.4 mV/K × 273 K = 109.2 V
The final volume = 0.4 mV/K × 473 K = 189.2 V
the instrument’s response as a function of time for a sudden temperature increase can be computed as follows:
Let consider y to be the function of time i.e y(t).
So;
y(t) = 109.2 + (189.2 - 109.2)( 1 - )mV
y(t) = (109.2 + 80 ( 1 - )) mV
Plot the response y(t) as a function of time.
The plot of y(t) as a function of time can be seen in the diagram attached below.
What are the units for y(t)?
The unit for y(t) is mV.
Find the 90% rise time for y(t90) and the error fraction,
The 90% rise time for y(t90) is as follows:
Initially 90% of 189.2 mV = 0.9 × 189.2 mV
= 170.28 mV
170.28 mV = (109.2 + 80 ( 1 - )) mV
170.28 mV - 109.2 mV = 80 ( 1 - )) mV
61.08 mV = 80 ( 1 - )) mV
0.7635 mV = ( 1 - )) mV
t = 1.44 × 25 × 10⁻³ s
t = 0.036 s
t = 36 ms
The error fraction =
The error fraction = 0.1
The error fraction = 10%
