Question 1

A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1$$, where $$x is in $$meters and $$t is in $$seconds. What is the car's velocity at $$t = 3 s$$?

Accepted Answer

$$v = 26 m/s$$

Question 2

A ball is thrown straight up with an initial velocity of $$20 m/s. $$Neglecting air resistance, what is the maximum height reached by the ball? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$20.4 m$$

Question 3

Which of the following best describes the meaning of the slope of a position vs. time ($$x vs$$. $$t) $$graph?

Accepted Answer

It represents the object's velocity.

Question 4

A runner moves with a constant velocity of $$5 m/s $$east for $$10 s$$, then turns around and runs $$5 m/s $$west for $$4 s. $$What is the runner's total displacement?

Accepted Answer

$$30 m$\,$$ east

Question 5

The area under a velocity vs. time ($$v vs$$. $$t) $$graph between $$t = 0 s $$and $$t = 5 s $$represents:

Accepted Answer

The object's displacement during that time interval.

Question 6

A projectile is launched horizontally from a $$45 m $$high cliff with a speed of $$10 m/s. $$How far from the base of the cliff does it land? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$30 m$$

Question 7

Which of the following is the correct method to find acceleration from a velocity vs. time ($$v vs$$. $$t) $$graph?

Accepted Answer

Calculate the slope of the $$v vs$$. $$t$$ graph.

Question 8

A student walks $$3 km $$north, then $$4 km $$east. What is the magnitude of the displacement vector?

Accepted Answer

$$5 km$$

Question 9

A car accelerates uniformly from rest to $$20 m/s in$$ $$5 s. $$What is its acceleration?

Accepted Answer

$$4$$ $$m/s^2$

Question 10

Which of the following statements about free-fall motion is correct (neglecting air resistance)?

Accepted Answer

All objects fall with the same constant acceleration regardless of their mass.

Question 11

A ball is thrown horizontally from a $$20 m $$high building with a speed of $$5 m/s. $$How long does it take to hit the ground? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$2.02 s$$

Question 12

Which of the following best describes the resultant vector when adding two vectors at right angles with magnitudes $$A$$ and $$B$$?

Accepted Answer

$$\sqrt{A^2$ + B^2$}$$

Question 13

A cyclist travels $$10 m $$east, then $$24 m $$north. What is the direction of the displacement vector relative to east?

Accepted Answer

$$67.4^\circ$$ north of east

Question 14

A motion diagram shows an object with equally spaced dots. What does this indicate about the object's motion?

Accepted Answer

The object is moving at constant velocity.

Question 15

A car moves with a velocity described by $$v(t) = 3t m/s. $$What is the displacement between $$t = 0 s $$and $$t = 4 s$$?

Accepted Answer

$$24 m$$

Question 16

A ball is dropped from rest from a height of $$80 m. $$How long does it take to reach the ground? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$4.04 s$$

Question 17

Which of the following is true about the displacement of an object?

Accepted Answer

It is the straight-line distance from the initial to the final position.

Question 18

A car slows down from $$30 m/s to$$ $$10 m/s in$$ $$4 s. $$What is its acceleration?

Accepted Answer

$$-5$$ $$m/s^2$

Question 19

A projectile is launched at $$20 m/s at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$10 m/s$$

Question 20

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Velocity has direction, speed does not.

Kinematics and Vectors: Study Notes for Introductory Physics

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