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

$$v = 26 m/s$,\text{ where } v = \frac{dx}{dt} = 8t + 2$$

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

$$h = 20.4 m$,\text{ where } h = \frac{v_0$^2}{2g}$$

Q: A projectile is launched horizontally from a $$45 m $$high cliff with a speed of $$10 m/s. $$How long does it take to hit the ground? (Ignore air resistance, $$g = 9.8 m/s$^2.)$$

$$t = 3.03 s$,\text{ where } t = \sqrt{\frac{2h}{g}}$$

Q: A car travels east at $$30 m/s $$for $$10 s$$, then west at $$20 m/s $$for $$5 s. $$What is the car's average velocity over the entire trip?

$$\frac{200}{15} m/s$,\text{ where } v_{avg} = \frac{\Delta x}{\Delta t}$$

Q: A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of the vector?

$$5$$,\text{ where } |\vec{A}| = \sqrt{A_$$x^2 + A$$_$$y^2$$}$

Question 1

Which of the following best describes the difference between average velocity and instantaneous velocity?

Accepted Answer

Average velocity is the total displacement divided by total time, while instantaneous velocity is the velocity at a specific moment in time.

Question 2

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

Accepted Answer

$$v = 26 m/s$,	ext{ where } v = \frac{dx}{dt} = 8t + 2$$

Question 3

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Question 4

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

Accepted Answer

$$h = 20.4 m$,	ext{ where } h = \frac{v_0$^2}{2g}$$

Question 5

Which of the following is a correct representation of the area under a velocity vs. time graph?

Accepted Answer

It represents the object's displacement.

Question 6

A runner accelerates uniformly from rest to a speed of $$8 m/s in$$ $$4$$ seconds. What is the runner's acceleration?

Accepted Answer

$$a = 1 m/s$^2$$

Question 7

A projectile is launched horizontally from a $$45 m $$high cliff with a speed of $$10 m/s. $$How long does it take to hit the ground? (Ignore air resistance, $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$t = 3.03 s$,	ext{ where } t = \sqrt{\frac{2h}{g}}$$

Question 8

Which of the following best describes the particle model in physics?

Accepted Answer

It treats objects as point masses, ignoring their size and shape.

Question 9

A car travels east at $$30 m/s $$for $$10 s$$, then west at $$20 m/s $$for $$5 s. $$What is the car's average velocity over the entire trip?

Accepted Answer

$$\frac{200}{15} m/s$,	ext{ where } v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 10

Which of the following is NOT a correct use of significant figures?

Accepted Answer

Reporting a calculated value as $$3.141592653$$ when the input data had only two significant figures.

Question 11

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of the vector?

Accepted Answer

$$5$$,	ext{ where } |\vec{A}| = \sqrt{A_$$x^2 + A$$_$$y^2$$}$

Question 12

A cyclist rides $$5 km $$north, then $$12 km $$east. What is the magnitude of the cyclist's displacement?

Accepted Answer

$$13 km$,	ext{ where } d = \sqrt{5^2$ + 12^2$}$$

Question 13

Which of the following is a correct order-of-magnitude estimate for the mass of a car?

Accepted Answer

$$10^3 kg$,	ext{ or about 1000 kg}$$

Question 14

A ball rolls down a ramp with constant acceleration. If it starts from rest and travels $$8 m in$$ $$4 s$$, what is its acceleration?

Accepted Answer

$$a = 1 m/s$^2$$,	ext{ where } x = \frac{1}{2} a $$t^2$

Question 15

Which of the following is true about the sign of acceleration?

Accepted Answer

The sign of acceleration depends on the chosen coordinate system.

Question 16

A boat moves north at $$5 m/s $$relative to the water. The river flows east at $$3 m/s. $$What is the boat's speed relative to the ground?

Accepted Answer

$$\sqrt{34} m/s$,	ext{ where } v = \sqrt{5^2$ + 3^2$}$$

Question 17

Which of the following is a correct statement about projectile motion (ignoring air resistance)?

Accepted Answer

The horizontal and vertical motions are independent of each other.

Physics with Calculus: Motion, Kinematics, and Vectors (Exam 1 Study Guide)

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