Question 1

Which of the following best describes the definition of average velocity?

Accepted Answer

The displacement divided by the total time taken.

Question 2

Given the position function $$x(t) = 4t^2$ - 2t + 3$$, what is the instantaneous velocity at $$t = 2 s$$?

Accepted Answer

$$v = 14 m/s$$

Question 3

Which of the following equations correctly represents the acceleration as the second derivative of position with respect to time?

Accepted Answer

$$a = \frac{d^2$x}{dt^2$}$$

Question 4

A car moves along a straight road such that its velocity is given by $$v(t) = 3t^2$. What is the acceleration at t = 2$ s?

Accepted Answer

$$a = 12 m/s$^2$$

Question 5

If a particle starts from rest and moves with a constant acceleration $$a$$, which equation gives its position as a function of time?

Accepted Answer

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

Question 6

A ball is thrown vertically upward 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 7

Which of the following statements is true for an object in free fall near the Earth's surface?

Accepted Answer

The acceleration is constant and directed downward.

Question 8

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

Accepted Answer

$$2 m/s$^2$$

Question 9

If the velocity of a particle is given by $$v(t) = 5 - 2t$$, at what time does the particle come to rest?

Accepted Answer

$$t = 2.5 s$$

Question 10

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

Accepted Answer

$$12 m/s$\ 	ext{east}$$

Question 11

Which of the following is the correct unit for acceleration?

Accepted Answer

$$	ext{m/s}^2$$

Question 12

A cyclist starts from rest and accelerates at $$1 m/s$^2$$ for $$10$$ seconds. What is the final velocity?

Accepted Answer

$$10 m/s$$

Question 13

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

Accepted Answer

Speed is a scalar, velocity is a vector.

Question 14

A car accelerates from $$10 m/s to$$ $$30 m/s in$$ $$5$$ seconds. What is the average acceleration?

Accepted Answer

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

Question 15

If $$x(t) = 2t^3$ - 5t^2$ + 4t$$, what is the acceleration at $$t = 1 s$$?

Accepted Answer

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

Units, Physical Quantities, and Dimensional Analysis

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