Q: A vector $$\vec{A}$$ makes an angle $$\theta$$ with the x-axis. What are its x and y components?

$$A_x = A \cos \theta$$, $$A_y = A \sin \theta$$

Question 1

A ball is thrown straight up with an initial velocity of $$7.3\ \mathrm{m/s}$$ from a height of $$1.5\ \mathrm{m}$$ above the ground. What is the maximum height the ball reaches above the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$4.2\ \mathrm{m}$$

Question 2

Which of the following best describes the acceleration of a ball at the peak of its trajectory when thrown straight upward (neglecting air resistance)?

Accepted Answer

The acceleration is downward and equal to $$g.$$

Question 3

A car accelerates from rest with a constant acceleration $$a. $$Which of the following graphs best represents its velocity versus time?

Accepted Answer

A straight line with positive slope starting from the origin.

Question 4

Given the velocity function $$v(t) = v_0$ + at$$, what is the position function $$x(t)$$ for an object starting at $$x_0$$?

Accepted Answer

$$x(t) = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 5

A car crash reduces a car's velocity by $$87\ \mathrm{km/h} in$$ $$150\ \mathrm{ms}. $$What is the average acceleration in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$-161\ \mathrm{m/s^2$}$$

Question 6

Which of the following statements about vectors is correct?

Accepted Answer

A vector has both magnitude and direction.

Question 7

If the position of an object is given by $$x(t) = x_0$ + v_0$ t + \frac{1}{2} a t^2$, what is the instantaneous velocity at time t$?

Accepted Answer

$$v(t) = v_0$ + at$$

Question 8

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

Accepted Answer

$$5$$

Question 9

A ball is dropped from rest from a height $$h. $$Neglecting air resistance, which of the following is true about its velocity and acceleration just before it hits the ground?

Accepted Answer

Velocity is negative and acceleration is $$-g.$$

Question 10

Which of the following is the correct equation relating velocity, acceleration, and displacement for constant acceleration?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 11

A ball is thrown upward and returns to the same height. Which of the following best describes the velocity and acceleration at the highest point?

Accepted Answer

Velocity is zero, acceleration is $$-g.$$

Question 12

A car is at rest. The accelerator is pressed and held, causing constant acceleration. Which graph best represents the position versus time?

Accepted Answer

A curve that gets steeper with time (parabola).

Question 13

Which of the following is true about the addition of vectors?

Accepted Answer

Vector addition is commutative and associative.

Question 14

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the x-axis. What are its x and y components?

Accepted Answer

$$A_x = A \cos 	heta$$, $$A_y = A \sin 	heta$$

Question 15

A car crash test shows a velocity change from $$-22.3\ \mathrm{km/h} to$$ $$-45.5\ \mathrm{km/h} in$$ $$10\ \mathrm{ms}. $$What is the approximate instantaneous acceleration in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$-644\ \mathrm{m/s^2$}$$

Question 16

Which of the following best describes the relationship between position, velocity, and acceleration?

Accepted Answer

Velocity is the rate of change of position; acceleration is the rate of change of velocity.

Question 17

A ball is thrown upward. Neglecting air resistance, what is the direction of acceleration while the ball is in the air?

Accepted Answer

Always downward.

Physics with Calculus: Motion, Acceleration, and Vectors Study Guidance

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