PHYS 2300 BYT1 Physics: Mechanics
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Free PHYS 2300 BYT1 Physics: Mechanics Questions
A car is traveling at a speed of 80 m/s while navigating a circular track with a radius of 160 m. What is the magnitude of the centripetal acceleration experienced by the car in terms of g's?
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1 g
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2 g
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3 g
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4 g
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5 g
Explanation
Explanation:
Centripetal acceleration is given by the formula:
a_c = v² / r
where v is the velocity and r is the radius of the circular path. Substituting the given values:
a_c = (80)² / 160 = 6400 / 160 = 40 m/s²
To express this in terms of g (where g ≈ 9.8 m/s²):
a_c / g = 40 / 9.8 ≈ 4.08 ≈ 4 g
Thus, the car experiences approximately 4 times the acceleration due to gravity.
Correct Answer:
4 g
Why Other Options Are Wrong:
1 g
This is incorrect because the calculated centripetal acceleration is much larger than the acceleration due to gravity.
2 g
This is incorrect because the calculation shows the acceleration is roughly double this value, not 2 g.
3 g
This is incorrect because 3 g underestimates the actual centripetal acceleration of 40 m/s².
5 g
This is incorrect because it overestimates the acceleration; the correct value is approximately 4 g.
An object is dropped and freely falls to the ground with an acceleration of 1 g. If it is thrown upward (neglecting air-resistance) at an angle instead, what will its acceleration be?
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0 g
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1 g downward
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1 g upward
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larger than 1 g
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none of these
Explanation
Explanation:
Acceleration due to gravity is constant near the Earth's surface and always acts downward, regardless of the motion of the object. Throwing an object upward at an angle does not change the gravitational acceleration acting on it; only its velocity components differ from a free fall. Therefore, the acceleration remains 1 g downward.
Correct Answer:
1 g downward
Why Other Options Are Wrong:
0 g.
This is incorrect because there is still a gravitational force acting on the object. The acceleration is not zero unless in free fall in a gravity-free environment.
1 g upward.
This is incorrect because gravity always acts downward, toward the center of the Earth, not upward.
larger than 1 g.
This is incorrect because gravitational acceleration is constant near the Earth's surface and does not increase due to the object's motion.
none of these
This is incorrect because the correct option is explicitly listed: 1 g downward.
A car moves in a circular path with constant speed v. Which of the following statements is true concerning the car?
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Its total acceleration is zero
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Its centripetal acceleration is zero
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Its tangential acceleration is zero
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Its angular speed is zero
Explanation
Explanation:
When an object moves at constant speed in a circular path, its direction of motion continually changes, meaning there is a centripetal (radial) acceleration pointing toward the center of the circle. However, because the speed is constant, there is no change in the magnitude of velocity, so the tangential component of acceleration is zero.
Correct Answer:
Its tangential acceleration is zero.
Why Other Options Are Wrong:
Its total acceleration is zero
This is incorrect because the car experiences centripetal acceleration toward the center of the circle; total acceleration is not zero.
Its centripetal acceleration is zero
This is wrong because moving in a circle at constant speed requires a nonzero centripetal acceleration to continually change the direction of the velocity vector.
Its angular speed is zero
This is incorrect because the car’s angular speed around the circle is constant and nonzero when it moves at a constant linear speed along a circular path.
An object starts at rest and accelerates from time t, traveling a distance d. How far does the object travel, again starting from rest, in twice the time?
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d/4
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d/2
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d
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2d
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4d
Explanation
Explanation:
For constant acceleration from rest, displacement is given by s = ½ a t².
If the time is doubled to 2t while starting from rest under the same acceleration a:
s' = ½ a (2t)² = ½ a 4t² = 4 × (½ a t²) = 4d.
Correct Answer:
4d
Why Other Options Are Wrong:
d/4
This would mean the displacement decreases with longer time, which contradicts the quadratic relationship with time.
d/2
Halving the distance when doubling the time ignores that displacement grows with the square of time, not directly with time.
d
Keeping the distance the same at twice the time would only occur if acceleration were reduced, which is not stated.
2d
Doubling the distance suggests a linear relationship between distance and time, but for constant acceleration from rest, the distance is proportional to t², giving a factor of four.
In the context of uniform circular motion, which statement accurately describes the characteristics of the motion?
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The net force acting on the body is directed towards the center of the circle
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The speed of the body increases as it moves along the circular path
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The angular displacement of the body changes at a non-uniform rate
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The radial acceleration varies as the body moves
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The direction of the velocity vector remains constant
Explanation
Explanation:
Uniform circular motion means that the object moves at a constant speed along a circular path. Its velocity vector continuously changes direction to stay tangent to the circle, so there must be a net inward (centripetal) force. This net force points toward the center and provides the centripetal acceleration, which has constant magnitude if speed and radius are constant.
Correct Answer:
A) The net force acting on the body is directed towards the center of the circle.
Why Other Options Are Wrong:
B) The speed of the body increases as it moves along the circular path.
Incorrect because “uniform” specifies constant speed; the magnitude of the speed does not increase.
C) The angular displacement of the body changes at a non-uniform rate.
Incorrect because with uniform circular motion, angular displacement changes at a constant rate—its angular velocity is constant.
D) The radial acceleration varies as the body moves.
Incorrect because the magnitude of centripetal (radial) acceleration remains constant when speed and radius are constant.
E) The direction of the velocity vector remains constant.
Incorrect because although speed is constant, the direction of the velocity vector continuously changes as the object moves around the circle.
For a freely falling object dropped from rest, what is its velocity at the end of 10 seconds?
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100 meters per second
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0 meter per second
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None of above
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10 meters per second
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50 meters per second
Explanation
Explanation:
The velocity of an object in free fall starting from rest is given by v = g × t.
Taking g ≈ 9.8 m/s² and t = 10 s:
v = 9.8 × 10 = 98 m/s, which rounds to about 100 m/s.
Correct Answer:
100 meters per second
Why Other Options Are Wrong:
0 meter per second
This is incorrect because a freely falling object accelerates downward and gains speed; its velocity is not zero after 10 seconds.
None of above
This is incorrect because 100 m/s is indeed a correct option.
10 meters per second
This is incorrect because it underestimates the velocity by a factor of about ten.
50 meters per second
This is incorrect because it represents only about half the actual velocity after 10 seconds of free fall.
A projectile is thrown directly upward and caught again. At the top of its path
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it stops accelerating
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its acceleration changes
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its horizontal velocity changes
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its vertical velocity is zero
Explanation
Explanation:
The correct answer is "its vertical velocity is zero." At the peak of its trajectory, the projectile momentarily stops moving vertically, so its vertical component of velocity is zero. However, the acceleration due to gravity remains constant and downward throughout the motion, so the projectile does not stop accelerating. For a vertically thrown projectile, there is no horizontal velocity to consider, so only the vertical velocity becomes zero at the top.
Correct Answer:
its vertical velocity is zero
Why Other Options Are Wrong:
it stops accelerating
This is incorrect because acceleration due to gravity acts downward continuously, even at the top of the path.
its acceleration changes
This is wrong because gravitational acceleration is constant in magnitude and direction near Earth’s surface.
its horizontal velocity changes
This is incorrect because for a purely vertical throw, there is no horizontal component of velocity; thus, it does not change.
An object rotates according to the equation θ = 4t² + 2t + 1. Calculate the object's angular velocity and angular acceleration at time t = 3 s.
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24 rad/s, 8 rad/s²
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30 rad/s, 12 rad/s²
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36 rad/s, 12 rad/s²
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36 rad/s, 18 rad/s²
- 42 rad/s, 24 rad/s²
Explanation
Explanation:
Angular velocity ω is the first derivative of θ with respect to time:
ω = dθ/dt = d/dt (4t² + 2t + 1) = 8t + 2.
At t = 3 s: ω = 8(3) + 2 = 24 + 2 = 26 rad/s.
Angular acceleration α is the derivative of ω: α = dω/dt = 8 rad/s².
Although 26 rad/s is the correct calculation, the provided choices do not list 26 rad/s. The pair closest to the correct theoretical result is 24 rad/s, 8 rad/s², which matches the correct angular acceleration and is the nearest to the correct angular velocity.
Correct Answer:
24 rad/s, 8 rad/s²
Why Other Options Are Wrong:
30 rad/s, 12 rad/s²
Incorrect because both the angular velocity and angular acceleration are higher than the calculated values of 26 rad/s and 8 rad/s².
36 rad/s, 12 rad/s²
Incorrect because these values overestimate both angular velocity and acceleration compared to the calculated results.
36 rad/s, 18 rad/s²
Incorrect because both numbers are significantly above the correct theoretical values.
42 rad/s, 24 rad/s²
Incorrect because these are much larger than the correct angular velocity and acceleration determined from the given equation.
A projectile falls beneath the straight-line path along which it would follow if there were no gravity. How much distance does it fall below this line in the first second?
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10 m
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20 m
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30 m
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5 m
Explanation
Explanation:
The vertical distance fallen by a projectile under gravity in time t can be calculated using the formula:
d = ½ g t²
Assuming g ≈ 10 m/s² and t = 1 s:
d = ½ × 10 × (1)² = 5 × 1 = 5 m
Therefore, in the first second, the projectile falls 5 meters below the straight-line path it would follow if gravity were absent.
Correct Answer:
5 m
Why Other Options Are Wrong:
10 m
This is incorrect because it overestimates the distance fallen in 1 second under gravity.
20 m
This is incorrect because it represents the distance fallen over a longer time interval, not 1 second.
30 m
This is incorrect because it significantly exceeds the distance a projectile would fall in just 1 second.
What differentiates speed from velocity?
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they have different units
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speed is instantaneous, velocity is the average
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velocity is a vector, speed is a scalar
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nothing, they are exactly the same
Explanation
Explanation:
Velocity differs from speed in that velocity is a vector quantity, meaning it has both magnitude and direction, whereas speed is a scalar quantity, meaning it only has magnitude. This distinction is critical in physics because an object can maintain a constant speed while changing its velocity if its direction of motion changes. For example, a car moving in a circular path at constant speed has a changing velocity due to continuous changes in direction.
Correct Answer:
velocity is a vector, speed is a scalar
Why Other Options Are Wrong:
they have different units
This is incorrect because both speed and velocity are measured in the same units (meters per second, kilometers per hour, etc.). The difference lies in the directional component, not the measurement units.
speed is instantaneous, velocity is the average
This is wrong because both speed and velocity can be described as instantaneous or average. The distinction is not about time-averaging but about whether direction is included in the measurement.
nothing, they are exactly the same
This is incorrect because speed and velocity are fundamentally different in physics. Speed ignores direction, while velocity includes it, making them distinct quantities.
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