2D Kinematic Not Constant Acceleration

An object free-falls from rest a distance D in a given amount of time. How far will the same object fall from rest in twice the elapsed time?

• D

• 2 D

• 4 D

Answer explanation

Tags

NGSS.HS-PS2-1

An object's position vs. time is depicted in the graph above. Based on the graph, at which time points will the object's velocity be closest to zero?

• 0 s and 2 s

• 0 s and 4 s

• 1 s and 2 s

• 1 s and 3 s

Answer explanation

When a position-time graph is horizontal, the velocity of the object is zero. The velocity at any instant in time is the slope of the line tangent to any point on the position-time graph. For this graph, that occurs at 1 s and 3 s.

Which of the following best describes the motion of the car in regions C, D, and E of the velocity versus time graph?

• It is slowing down until it reverses direction and speeds back up again.

• It moves at a constant velocity in the negative direction.

• It accelerates at a constant, nonzero acceleration except at point C when its acceleration is zero.

• Its position changes at a constant rate.

Answer explanation

At the beginning of region C, the velocity gradually decreases to zero, indicating its speed is decreasing. At point D, the velocity has reached zero (resting instantaneously). At the beginning of region E, the negative velocity indicates that the direction is now negative, and the increasing magnitude of the velocity indicates it is speeding up.

Tags

NGSS.HS-PS2-1

Which of the following best ranks the displacement of the car in each region of the graph above?

• A > B > C > D

• A > C > B > D

• D > A > C > B

• A > C > D > B

Answer explanation

The displacement is the final position minus the starting position.

The displacement for part A is 125 m - 0 m = +125 m.

The displacement for part B is 100 m - 100 m = 0 m.

The displacement for part C is 125 m - 100 m = +25 m.

The displacement for part D is 0 m - 125 m = - 125 m.

Which of the following are moving at a constant velocity? Select two.

• A tetherball moving in a circle at a constant speed

• A rolling ball constantly accelerating at - 0.20 m/s2

• A jogger continuing to run at a speed of 2 m/s along a straight path

• A box steadily sliding down an incline at a speed of 0.5 m/s

Tags

NGSS.HS-PS2-2

Which of the following best ranks the average speed of the car in each region of the graph?

• A > B > C > D

• A > C > B > D

• D > A > C > B

• A > C > D > B

Answer explanation

The average speed is the distance traveled divided by the time for each section.

The average speed for part A is (125 m) /10 s = 12.5 m/s.

The average speed for part B is (0 m)/5 s = 0 m/s.The average speed for part C is (25 m) /5 s = 5 m/s.

The average speed for part D is (125 m) /5 s = 25 m/s.

Which of the following are moving with a constant, nonzero acceleration? Select two.

• A skydiver gaining speed as she falls through the air

• A hammer falling near the surface of the moon

• A truck moving in a circle as it gains 3 m/s each second

• A cart moving in a straight line gaining 3 m/s each second

Answer explanation

Tags

NGSS.HS-PS2-1

Which of the following are true about the motion of the carts in the graph?

• At the 7-second clock reading, Cart 1 is moving with the same speed as Cart 2.

• Cart 1 moves at a constant speed in the negative direction.

• Cart 1 moves in the negative direction over the entire 8-second trip.

• At the 8-second clock reading, Cart 1 was moving faster than Cart 2.

Answer explanation

Option A is correct because speed is the absolute value of velocity, and both carts were moving at 4 m/s. Option D is also correct because, at the 8-second clock reading, Cart 1 was moving at 6 m/s and Cart 2 was moving at 4 m/s. Option C is tempting but incorrect because it had positive velocity for the first half of the trip, indicating that it was moving in the positive direction.

An object is free-falling near the surface of the Earth. At a certain instant in time, it is falling downward at a rate 25 m/s. Two seconds later, what are its instantaneous speed and acceleration, respectively?

• 
• 
• 
• 

Answer explanation

The free-fall acceleration near the surface of the Earth is a uniform rate of 10 m/s?, meaning each and every second its speed increases by 10 m/s. In two seconds of time, its speed will increase to 25 m/s + 10 m/s + 10 m/s = 45 m/s.

Tags

NGSS.HS-PS2-1

An object at the 35-m position of a one-dimensional coordinate system is moving in the negative direction at a constant speed of 25 m/s. Which function below best represents how the car's position (X) in meters on the coordinate system changes with time (t)?

• X=-25t + 35

• X=-35t + 25

Answer explanation

At a constant speed, position should change linearly with time,

so only options A and B should be considered. At t = 0, option A's position

is 35 m. Each second after that, its position changes by -25 m each second.