In the graph above, what is the instantaneous speed of the object after the first five seconds?
1 answer:
Answer:
D) 25 m/s
Explanation:
In order to solve this problem we must use the following kinematics equation.
where:
Vf = final speed [m/s]
Vi = initial speed = 0
a = acceleration = 5[m/s^2]
t = time = 5[s]
After 5 seconds the acceleration is equal to 5 [m/s^2]
Now replacing the values in the equation:
Vf = 0 + (5*5)
Vf = 25[m/s]
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Answer:
0.1 m/s
Explanation:
Please see attached photo for explanation.
Mass of 1st cart (m₁) = 500 g
Initial velocity of 1st cart (u₁) = 0.25 m/s
Mass of 2nd cart (m₂) = 750 g
Initial velocity of 2nd cart (u₂) = 0 m/s
Velocity (v) after collision =.?
m₁u₁ + m₂u₂ = v(m₁ + m₂)
(500 × 0.25) + (750 × 0) = v(500 + 750)
125 + 0 = v(1250)
125 = 1250v
Divide both side by 1250
v = 125 / 1250
v = 0.1 m/s
Thus, the two cart will move with a velocity of 0.1 m/s after collision.
Answer:
The answer to the question is;
The required torque that it would take to cause the gyroscopes to precess through an angle of 1.0×10−6 degree during a 5.0-hour exposure of a galaxy is 2.44 ×10⁻¹² N·m
Explanation:
To solve the question we first resolve the units of the given quantities as follows
The gyroscopes spin at 19,200 rpm that is 19,200 revolutions per minute
1 revolution = 2π rad and
1 minute = 60 seconds
Therefore 19,200 revolutions per minute = 2π×19,200÷60 rad/s
= 2010.619 rad/s
The angle of precess is given as 1.0×10⁻⁶ °. We convert the angle to radians as follows
360 ° = 2π radians
1 ° = radians and
1.0×10⁻⁶ ° = radians × 1.0×10⁻⁶ ° = 1.745×10⁻⁸ rad
To find the torque we note that the torque is given by
Precession angular speed × The moment of inertia × angular velocity
The precession angular speed is given by
The precession angle was determined in rad as 1.745×10⁻⁸ rad
The precession time is 5 hours which is equal to 5×60×60 = 18000 s
Therefore the precession velocity = = 9.696×10⁻¹³ rad/s
The moment of inertia is given by
Formula for the moment of inertia of a thin walled cylinder I = m·r²
Where:
r = Radius of the gyroscope = Diameter/2 = 5.0 cm/2 = 2.5 cm = 0.025 m
m = Mass of each gyroscopes = 2.0 kg
Therefore I = m·r² = 2.0 kg × (0.025 m)² = 0.00125 kg·m²
Torque, τ = Ω·I·ω
Where:
Ω = Precession velocity = 9.696×10⁻¹³ rad/s
I = Moment of inertia = 0.00125 kg·m²
ω = Angular speed = 2010.619 rad/s
τ = 9.696×10⁻¹³ rad/s × 0.00125 kg·m² × 2010.619 rad/s =
2.44 ×10⁻¹² kg·m²/ s² = 2.44 ×10⁻¹² N·m
The required torque is 2.44 ×10⁻¹² N·m.