Q: A hiker walks in two stages: $$\vec{D}_1 = (2\hat{i} + 5\hat{j}) m $$and $$\vec{D}_2 = (3\hat{i} - 1\hat{j}) m. $$What is the scalar (dot) product $$\vec{D}_1 \cdot \vec{D}_2$$?

$$(2 \times 3) + (5 \times -1) = 6 - 5 = 1 m$^2$$

Question 1

Which of the following is the correct dimensional formula for velocity?

Accepted Answer

$$[L][T]^{-1}$$

Question 2

A velocity-time graph for an object shows a flat, horizontal line at $$v = 5 m/s $$between $$t = 2 s $$and $$t = 6 s. $$Which statement is true about the object's motion during this interval?

Accepted Answer

The object has zero acceleration.

Question 3

A remote-control car has a velocity vector $$\vec{v} = (6\hat{i} - 8\hat{j}) m/s. $$What is the magnitude of the car's speed?

Accepted Answer

$$10 m/s$$

Question 4

A heavy box is pushed across a horizontal floor at constant speed in a straight line. Which statement about the forces acting on the box is correct?

Accepted Answer

The net force on the box is zero.

Question 5

A baseball is thrown straight upward. At the very peak of its flight, which of the following is true?

Accepted Answer

Its velocity is zero, and its acceleration is $$9.8 m/s$^2$$ downward.

Question 6

What is $$5 	imes 10^4$ written to three significant figures?

Accepted Answer

$$5.00 	imes 10^4$

Question 7

A hiker walks in two stages: $$\vec{D}_1 = (2\hat{i} + 5\hat{j}) m $$and $$\vec{D}_2 = (3\hat{i} - 1\hat{j}) m. $$What is the resultant displacement vector $$\vec{D}_{	ext{total}} = \vec{D}_1 + \vec{D}_2$$?

Accepted Answer

$$(5\hat{i} + 4\hat{j}) m$$

Question 8

A car drives horizontally off a $$20 m $$high cliff at $$15 m/s. $$Neglecting air resistance, how long is the car in the air before it hits the ground?

Accepted Answer

$$2.02 s$$

Question 9

A car traveling at $$25 m/s $$comes to a complete stop in $$3.5 s $$with constant deceleration. What is the magnitude of the car's acceleration?

Accepted Answer

$$7.14$$ $$m/s^2$

Question 10

A $$40 kg $$box is pulled with a force of $$150 N at an $$angle of $$30^	ext{o}$$ above the horizontal on a frictionless floor. What is the horizontal acceleration of the box?

Accepted Answer

$$2.60 m/s$^2$$

Question 11

A child of mass $$20 kg $$rides down a frictionless hill inclined at $$30^	ext{o}. $$What is the acceleration of the child?

Accepted Answer

$$4.9 m/s$^2$$

Question 12

A ball is launched horizontally from a height of $$4 m $$with an initial velocity of $$5 m/s. $$How much time does it take to reach the floor?

Accepted Answer

$$0.90 s$$

Question 13

A hiker walks in two stages: $$\vec{D}_1 = (2\hat{i} + 5\hat{j}) m $$and $$\vec{D}_2 = (3\hat{i} - 1\hat{j}) m. $$What is the scalar (dot) product $$\vec{D}_1 \cdot \vec{D}_2$$?

Accepted Answer

$$(2 	imes 3) + (5 	imes -1) = 6 - 5 = 1 m$^2$$

Question 14

A $$40 kg $$box is pulled with a force of $$150 N at an $$angle of $$30^	ext{o}$$ above the horizontal. What is the normal force acting on the box from the floor?

Accepted Answer

$$317 N$

Question 15

A car traveling at $$25 m/s $$comes to a complete stop in $$3.5 s $$with constant deceleration. How far does the car travel while braking?

Accepted Answer

$$43.75 m$$

Question 16

A child of mass $$20 kg $$rides down a frictionless hill inclined at $$30^	ext{o}. $$What is the normal force exerted on the child by the toboggan?

Accepted Answer

$$98 N$

Question 17

A ball is launched horizontally from a height of $$4 m $$with an initial velocity of $$5 m/s. $$How far horizontally does the ball reach on the floor?

Accepted Answer

$$4.5 m$

Question 18

A stunt driver drives a car horizontally off a $$20 m $$high cliff at $$15 m/s. $$What is the vertical component of the car's velocity just before it hits the ground?

Accepted Answer

$$19.8 m/s$$

Question 19

A stunt driver drives a car horizontally off a $$20 m $$high cliff at $$15 m/s. $$What is the magnitude of the car's total velocity just before impact?

Accepted Answer

$$24.7 m/s$$

Question 20

A hiker walks in two stages: $$\vec{D}_1 = (2\hat{i} + 5\hat{j}) m $$and $$\vec{D}_2 = (3\hat{i} - 1\hat{j}) m. $$What is the angle of the resultant displacement vector $$\vec{D}_{	ext{total}}$$ relative to the positive x-axis?

Accepted Answer

$$38.7^	ext{o}$$

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