Q: Which of the following is the correct definition of instantaneous velocity?

$$V_x = \lim_{\Delta T \to 0} \frac{\Delta x}{\Delta T}$$

Question 1

A car starts from rest and accelerates at $$2\ \mathrm{m/s^2$}$$ for $$5$$ seconds. What is its final velocity?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 2

Which equation gives the position $$x of an $$object moving with constant acceleration $$a_x$$ after time $$T$$, starting from initial position $$x_0$$ and initial velocity $$V_{0x}$$?

Accepted Answer

$$x = x_0$ + V_{0x} T + \frac{1}{2} a_x T^2$

Question 3

A train accelerates at $$0.5\ \mathrm{m/s^2$}$$ for $$60$$ seconds, then moves at constant speed for $$240$$ seconds, and finally slows down at $$-1.0\ \mathrm{m/s^2$}$$ for $$30$$ seconds. What is the train's speed at the end of the acceleration phase?

Accepted Answer

$$30\ \mathrm{m/s}$$

Question 4

Which of the following best describes 'free fall'?

Accepted Answer

Any motion where gravity is the only force acting on the object

Question 5

An object is thrown upward with initial velocity $$V_{0y}. $$Which equation gives its velocity after time $$t$$ under gravity $$g$$?

Accepted Answer

$$V_y = V_{0y} - g t$$

Question 6

A ball is dropped from a height of $$20\ \mathrm{m} on $$Earth ($$g = 9.81\ \mathrm{m/s^2$}). $$How long does it take to reach the ground? (Neglect air resistance)

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 7

Which equation relates the final velocity squared to initial velocity squared, acceleration, and displacement for constant acceleration?

Accepted Answer

$$V_x^2$ = V_{0x}^2 + 2 a_x \Delta x$$

Question 8

A runner moves with an initial velocity of $$5\ \mathrm{m/s}$$ and accelerates at $$1\ \mathrm{m/s^2$}$$ for $$10$$ seconds. What is the total displacement?

Accepted Answer

Question 9

On the Moon, the acceleration due to gravity is $$1.62\ \mathrm{m/s^2$}. If an $$astronaut drops a rock from rest, how far will it fall in $$3$$ seconds?

Accepted Answer

$$7.29\ \mathrm{m}$$

Question 10

Which of the following is the correct unit for acceleration?

Accepted Answer

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

Question 11

A cyclist slows down from $$12\ \mathrm{m/s} to$$ $$4\ \mathrm{m/s} in$$ $$4$$ seconds. What is the acceleration?

Accepted Answer

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

Question 12

Which scenario best represents 'slowing down' in terms of velocity and acceleration?

Accepted Answer

$$V_{2x} - V_{1x}  0$$

Question 13

A stone is thrown vertically upward with $$V_{0y} = 20\ \mathrm{m/s}. $$How long does it take to reach its highest point? ($$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.04\ \mathrm{s}$$

Question 14

Which equation gives the position $$y of an $$object under gravity after time $$t$$, starting from $$y_0$$ and initial velocity $$V_{0y}$$?

Accepted Answer

$$y = y_0$ + V_{0y} t - \frac{1}{2} g t^2$

Question 15

A train moves at a constant speed of $$30\ \mathrm{m/s}$$ for $$240$$ seconds. What is the distance covered during this interval?

Accepted Answer

$$7200\ \mathrm{m}$$

Question 16

Which of the following is the correct definition of instantaneous velocity?

Accepted Answer

$$V_x = \lim_{\Delta T 	o 0} \frac{\Delta x}{\Delta T}$$

Question 17

A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$10\ \mathrm{m}. $$How long does it take to hit the ground? ($$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

$$0.85\ \mathrm{s}$$

Question 18

Which of the following is NOT a correct kinematic equation for constant acceleration?

Accepted Answer

$$x = x_0$ + a_x T$$

Question 19

If an object moves with constant velocity, what is its acceleration?

Accepted Answer

$$0\ \mathrm{m/s^2$}$$

Kinematics: Motion Along a Straight Line and Free Fall

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