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Kinematics and Dynamics

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Kinematics and Dynamics

1) Question : Given 2 vectors (blue and green) and Red representing the resulting vector of Blue+ Green vector, which of the following correctly represents the resulting vector in Red

Top right

Top left

Explanation: This is the correct answer. We have the freedom to move the green vector as long as it stays parallel to the initial green vector. To make it easier to visualize, we first ensure that the base of the green vector touches the arrow of the blue vector, and then we connect the starting point and end point of the blue and green vectors respectively, eventually drawing the resulting vector.

Bottom left

bottom right

2) Question : Given 2 vectors (blue and green) and Red representing the resulting vector of Blue+ Green vector, which of the following correctly represents the resulting vector in Red

Top left

Explanation: This is the correct answer. You can freely change the position of the green arrow as long as it is parallel to the original green arrow. Here, the base of the green arrow touches the arrow of the blue end, which makes it reasonable to connect the starting point of the blue arrow and end point of the green arrow to ultimately get the resulting vector in Red

Bottom left

Top right

Bottom right

3) Question : Which of the following represents the value of sin α

Side B/ Side A

Side C/ Side A

Side C/ Side B

Side B/Side C

Explanation: This is the correct answer. (Remember, sin(α)= opposite/ hypotenuse, where opposite represents the side that is directly opposite to the alfa angle, while the hypotenuse represents the angle opposite to the right angle. In this case, side B and side C corresponds to the opposite and hypotenuse angles respectively.

4) Question : Which of the following represent the value of cos(α)

Side A/Side B

Side A/Side C

Explanation: This is the correct answer. Recall that cos(α) refers to adjacent over hypotenuse. Sides A and C represents the adjacent and hypotenuse sides respectively

Side B/ Side C

Side C/ Side A

5) Question : Which of the following represents the value of tan(α)

Side A/Side B

Side B/Side A

Explanation: This is the correct answer. Recall that Tan (α) refers to opposite divided by adjacent. In this case, Sides B and A are the opposite and adjacent respectively.

Side B/ Side C

Side A/Side C

Questions 6-10 represents are based on the diagram in

6) Question : If side A= 6 cm and side B= 4 cm, what is the value of side C in cm

7.2 cm

6.2 cm

5.2 cm

8.2 cm

7) Question : If side A= 6 cm and Side B = 8 cm, what is the value of Side C

Explanation: This is the correct answer.

8) Question : Given 𝐴 = 9 cm and C= 15 cm , find B

9) Question : In a 100 meter race, a horse travels the whole distance in 40 seconds, Find his speed in m/s

2.5 m/s

Explanation: Speed is equal to the distance covered divided by the seconds. Since the horse covered, 100 m in 40 seconds, this means their speed is 100m/40s, which translates into 2.5 m/s

400

4000

10) Question : In a 100 meter race, a horse travels the whole distance in 40 seconds, Find his speed in km/hr

0.9 km/hr

0.09 km/hr

9 km/hr

90 km/hr

11) Question : A person starts at their house and walks 40 meters east. They then decided to walk 15 meters west toward the direction of the house. What are the total distance traveled and the displacement from the house?

55 m, 15 m

15 m, 55 m

55 m, 25 m

Explanation: This is a tricky question. However, it is important to distinguish the difference between distance and displacement. Distance means the total meters the person traveled, while displacement represents their final position relative to the initial position. Since, they walked 40 m east and 15 m(back), their total distance covered is 55m. However, their final position is 40m-15 m= 25 m relative to their initial position, which represents their displacement.

25 m, 55 m

12) Question : A person starts at their house and walks 40 meters east. They then decided to return to their house. After the person returned back to their house, what is the total distance traveled and the displacement from the house?

80 m, 40 m

40m, 80 m

80 m, 80 m

80m , 0 m

Explanation: This is the correct answer. If the person walks 40 meters far from their house and then returned back, this means the total distance covered is 80 m. However, if they returned back, this means their final position is 0 m( same as their initial position).

13) Question : If the person walked 9 meters west and 16 meters north, what is their final distance and displacement covered respectively?

25 m, 15 m

10 m, 25 m

25 m, 10 m

Explanation: This is the correct answer. Recall distance is equal to 9+16=25 m( total meters covered), while displacement is the distance from the initial point to the end point. So, we have to use the Pythagoras theorem to calculate the displacement.

7 m, 10 m

14) Question : A sport car accelerates from 20 m/s to 60 m/s in 4 seconds, what is the magnitude of the acceleration?

160 m/s²

160 m/s

10 m/s²

Explanation: This is the correct answer. Acceleration measures the rate of change of velocity per second. Change of velocity= Vf-Vi= 40 m/s. Time= 4 seconds So, change of velocity/time= 40m/s divided by 4s= 10 m/s² not 10 m/s

10 m/s

15) Question : A person runs 40 m/s for a period of 4 seconds. What is the total distance covered during this time period.

160 m

Explanation: Distance= Velocity x seconds. In case you forgot the exact formula, you can simply use the units to deduce the value of the distance. Note that distance is measured by m, so we can multiply units 4m/s and s, so second and second can be eliminated and m is left. See the detailed calculation below.

160 s

10 m

10 s

16) Question : A person has 1 minute of fuel left and is 4500 m from their destination. They accelerate at 2 m/s², starting at 20 m/s at t=0 s. Will they make it to the distination?

No, since the total distance that can be covered<4500 m

Yes, since the maximum distance that can be covered>4500 m

Explanation: This is the correct answer. Mcat loves to test your conceptual understanding of the material. First, note that the context implies that the car can only move for 1 minute, which is equal to 60 seconds. If that is the case, we can use the formula, x-xo= Vot + 1/2at^2, where x represents final position and xo represents the initial position. It could be rewritten as x-xo, and thus corresponds to the distance covered for this case. Vo represents the initial speed taken at t=0 and a represents the acceleration. Apply this formula, you will get the maximum distance that can be covered in this 1 minute is 4800m, which is more than 4500 m. Thus, they can reach the 4500 m before running out of fuel. Lastly note, that for the formula to work, you should use the correct units as shown below.

No, since the total distance that can be covered>4500 m

Yes, since the maximum distance that can be covered<4500 m

17) Question : A soccer player shoots a ball with an initial velocity of 30 m/s and it constantly accelerates by 4m/s^2 If the ball has been kicked for 4 seconds, what is its final velocity?

46 m/s

Explanation: This is the correct answer. Use the equation, vf=vot+at, making sure you have the correct units as shown below.

34 m/s

36 m/s

44 m/s

18) Question : A table is initially at rest. It stays at rest unless an external force is acting on it. What Newton's law does it belong to?

Newton's first law

Explanation: Explanation: This is the correct answer choice. Newton's first law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and direction unless acted upon by an unbalanced external force. This means that objects resist changes in their state of motion. Newton's Second law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law defines how the motion of an object changes when a force is applied. Mathematical formula: Fnet=ma Newton's third law: For every action, there is an equal and opposite reaction. When one object exerts a force on a second object, the second object exerts an equal force back on the first object in the opposite direction. Mathematical formula: F 1 on 2 = -F 2 on 1

Newton's second Law

Newton's third law

None of the above

19) Question : Alex pushes a table with a force of 5 N, but the table does not move because the static friction opposes it with a force of 5N. Which Newton's law does it represent?

Newton's Second law

Newton's third law

Newton's first Law

Explanation: This is the correct answer. Even though there is a force exerted by Alex on the table, the table does not move because the Net Force acting on itis zero. So, the object will stay at rest unless acted by an unbalanced force.

None of the above

20) Question : A smart way swimmers use to initially swim faster is pressing their foot against the wall of the pool to give themselves a quick start. Which of the following does it represent?

Newton's first law

Newton's second Law

Newton's third law

Explanation: Newton's Third Law states that for every action, there is an equal and opposite reaction. When swimmers press their feet against the wall of the pool (the action force), the wall exerts an equal and opposite force back on their feet (the reaction force). This reaction force propels the swimmers forward, allowing them to start swimming faster.

None of the above

21) Question : You initially kicked a ball. After kicking it, it stays at a constant speed. While staying at a constant speed, Which Newton's law does it represent?

Newton's first law

Explanation: This is the correct answer. Staying at a constant speed implies there is no net force acting on it. Fnet=ma, and Fnet=0, indicating a=0, and ultimately constant velocity.

Newton's second law

Newton's third law

None of the above

22) Question : After kicking a ball, air resistance exerts an opposite force on its motion, which slows it down. Which of the following does it represent?

Newton's first law

Newton's Second law

Explanation: This is the correct answer. The ball slowed down, which fits the definition of this Law. Fnet=ma and there is a negative Fnet( friction force opposing the motion), so acceleration is negative.

Newton's third law

None of the above

23) Question : What does kinetic friction mean

the force that opposes the motion of two surfaces sliding past each other.

the force that resists the initiation of motion between two surfaces in contact

The force that prevents two surfaces from coming into contact.

The force that accelerates an object sliding on a surface

24) Question : Static Friction is:

The force that opposes the motion of an object already in motion.

The force that acts only when an object is in free fall.

The force that resists the initiation of motion between two stationary surfaces

The force that pushes an object to move faster on a rough surface