Q: Which formula correctly calculates average speed?

$$\text{Average speed} = \frac{\text{distance}}{\text{time}}$$

Q: Which of the following is the correct SI unit for acceleration?

$$\text{m} \cdot \text{s}^{-2}$$

Question 1

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total length of the path traveled, while displacement is the shortest straight-line distance from start to end, including direction.

Question 2

A runner jogs 80 m north, then 50 m east, then 70 m south. What is the magnitude of the runner's displacement from the starting point?

Accepted Answer

$$\sqrt{(80 - 70)^2$ + 50^2$} = \sqrt{100 + 2500} = \sqrt{2600} \approx 51 m$$

Question 3

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 4

A car travels 300 miles on a straight highway, then returns to its starting point. What is the car's total displacement?

Accepted Answer

$$0$$ miles

Question 5

A police car accelerates to $$60 m/s to $$catch a minivan moving at $$45 m/s$$, which is $$600$$ meters ahead. How long will it take the police car to catch up?

Accepted Answer

$$40$$ seconds

Question 6

Which formula correctly calculates average speed?

Accepted Answer

$$	ext{Average speed} = \frac{	ext{distance}}{	ext{time}}$$

Question 7

A boat travels east at $$5 m/s in a $$river with a current flowing north at $$3 m/s. $$What is the magnitude of the boat's resultant velocity?

Accepted Answer

$$\sqrt{5^2$ + 3^2$} = \sqrt{34} \approx 5.83 m/s$$

Question 8

A plane flies at $$80 mi/hr. $$What is its ground speed if it encounters a $$20 mi/hr $$headwind?

Accepted Answer

$$60 mi/hr$$

Question 9

Which of the following best describes velocity?

Accepted Answer

Velocity is a vector quantity describing the rate of change of displacement.

Question 10

A hiker walks $$100$$ meters at $$37^$$ north of east. What is the eastward (x) component of the displacement?

Accepted Answer

$$100 	imes \cos(37^)$$

Question 11

A person walks $$5$$ meters east, then $$1$$ meter west, and $$3$$ meters south. What is the magnitude of their displacement?

Accepted Answer

$$\sqrt{(5 - 1)^2$ + 3^2$} = \sqrt{16 + 9} = \sqrt{25} = 5 m$$

Question 12

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 13

A person walks $$40$$ meters north, then $$80$$ meters east. What is the magnitude of their displacement?

Accepted Answer

$$\sqrt{40^2$ + 80^2$} = \sqrt{1600 + 6400} = \sqrt{8000} \approx 89.4 m$$

Question 14

A car travels $$50$$ miles in $$3$$ hours. What is its average speed?

Accepted Answer

$$16.7$$ miles per hour

Question 15

Which equation is used to calculate displacement when two perpendicular components are known?

Accepted Answer

$$d = \sqrt{x^2$ + y^2$}$$

Question 16

A climber moves $$11,200$$ meters east and $$3,200$$ meters up from base camp to Camp A, then $$8,400$$ meters east and $$1,700$$ meters up to Camp B. What is the total displacement from base camp to Camp B?

Accepted Answer

$$\sqrt{(11,200 + 8,400)^2$ + (3,200 + 1,700)^2$} = \sqrt{19,600^2$ + 4,900^2$} \approx 20,200$$ meters

Question 17

Which of the following statements about speed and velocity is correct?

Accepted Answer

Velocity includes direction, while speed does not.

Question 18

A person walks $$100$$ meters at $$37^$$ north of east. What is the northward (y) component of the displacement?

Accepted Answer

$$100 	imes \sin(37^)$$

Question 19

Which of the following is the correct SI unit for acceleration?

Accepted Answer

$$	ext{m} \cdot 	ext{s}^{-2}$$

Speed, Velocity, Scalars, and Vectors: Fundamental Concepts in Kinematics

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