A proton moves along the x axis according to the equation x = 38 t + 14 t2, where x is in meters and t is in seconds. Calculate (a) the average velocity of the proton during the first 3.0 s of its motion, (b) the instantaneous velocity of the proton at t = 3.0 s, and (c) the instantaneous acceleration of the proton at t = 3.0 s.
Answers
Answer:
a) 240 m
b) 122 m/s
c) 28 m/s²
Explanation:
Given:
Equation for motion
x = 38t + 14t²
a) average velocity during first 3 seconds
average velocity =
now,
distance, at t = 0 s
x = 38 × 0 + 14 × 0² = 0 m
distance, at t = 3 s
x = 38 × 3 + 14 × 3² = 240 m
therefore,
average velocity = = 80 m/s
b) instantaneous velocity of the proton at t = 3.0 s
Instantaneous velocity, v =
or
Instantaneous velocity, v =
= 122 m/s
c) instantaneous acceleration of the proton at t = 3.0 s
Now,
Acceleration = = 0 + 28 = 28 m/s²
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the substance?
Answers
Where Q = Amount of heat in J
m = Mass of substance in kg
θ = Temperature rise in °C or K
C = Specific heat capacity in J/kgK
From given data:
Q = 33 kJ = 33 000 J, m= 2.0 kg, θ = 80 K, c = ?
33000 = 2 * c * 80
33000 = 160c
160c = 33000
c = 33000/160 = 206.25
Therefore specific heat capacity is 206.25 J/kgK
b.) how long will it take for the swimmer to cross the river, if the distance from the starting point to the dock is 300 m?
Please show all your work, thanks
Answers
a)The direction that she must aim herself through the water to arrive at the dock will be 73.7°.
b)The time it takes for the swimmer to cross the river will be 240 seconds.
What is speed?
Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.
Given data;
The maximum speed of the swimmer In still water,v=1.25m/s.
Speed of river = 0.35m/s [E]
α is the direction that she must aim herself through the water to arrive at the dock.
t is the time it takes for the swimmer to cross the river
The distance from the starting point to the dock is,s = 300 m
If the swimmer were to swim straight, the water's speed along the x-axis would have to match that of the swimmer.
α is the angle between vx and v
The value of the
The time that the swimmer will use for reaching the dock;
s = V×t
t = s/(v)
t=300 m / 1.25 m/sec
t = 240 seconds
Hence, the direction that she must aim herself through the water to arrive at the dock. and it takes for the swimmer to cross the river will be 73.7° and 240 seconds respectively.
To learn more about the speed refer to the link;
#SPJ2
Explanation:
As you can see in the picture, we want the swimmer to go on a straight line, so the speed of the water must be equal to the speed of the swimmer along the x-axis. We also know the value of v, so we can calculate the of the cosine of the angle (alpha) between Vx and V. Thanks to the fundamental relation of gioniometry (cos^2(x) + sin^2(x) = 1) we can find the sine of alpha and calculate Vy. With Vy we can calculate the time that the swimmer will use for reaching the dock: s = Vy * t => t = s/(Vy).
I'll let you do all the calculations, you just have to plug in values.
B) 3.06 × 107 J
C) 2.46 × 1015 J
D) 6.30 × 1015 J
E) 8.82 × 1015 J
Answers
Answer:
1.1025×10^15Joules
No correct option
Explanation:
The type of energy possessed by the object is kinetic energy. Kinetic energy is the energy due to virtue of an object motion.
KE = 1/2MV² where;
M is the mass of the car = 0.05kg
V is the velocity of the car
Since the car is traveling at 0.7c (c is the speed of light)
speed = 0.7c { 0.7(3×10^8)}
Speed = 2.1×10^8
Substituting this values in the formula given we have;
KE = 1/2×0.05×(2.1×10^8)²
KE = 1.1025×10^15Joules
No correct option.
Answers
Answer:
The baseball will accelerate.
Explanation:
According to Newton's second law,
The force is the product of the mass and acceleration of the object.
In mathematically term
Where, m = mass
a = acceleration
If we hit a baseball with a bat it will accelerate by the applied force.
Hence, The baseball will accelerate.
Answers
Answer:
Force exerted on the car is 7030 N.
Explanation:
It is given that,
Mass of the car, m = 740 kg
Initial speed of the car, u = 19 m/s
Final speed of the car, v = 0
Time taken, t = 2 s
Let F is the force exerted on the car during this stop. We know that it is equal to the product of force and acceleration. Mathematically, it is given as :
F = -7030 N
So, the force exerted on the car during this stop is 7030 N. Hence, this is the required solution.
acceleration = change_in_velocity / time
so:
force = 740 kg * (19 m/s - 0 m/s) / 2.0 s
= 740 * 19 / 2 kg m per second^{2}
= 7030 kg m per second^{2}
= 7030 newtons of force
Answers
Hope this helps :)
The law of conservation of momentum states that the total momentum of a closed system does not change. This means that when two objects collide the total momentum of the objects before the collision is the same as the total momentum of the objects after the collision.
Total momentum meansthe momentum of object 1 plus the momentum of object 2.Object 1 might not have the same momentum before and afterthe collisionbut the amount of momentum object 1 gains from the collisionis the same as the amount of momentum object 2 losesso the total momentum remains the same whether the collision is elastic or inelastic.The total momentum is also the same before and after an explosion.