Question 1

Which of the following best describes the instantaneous x-velocity $$v_x of a $$particle in straight-line motion?

Accepted Answer

It is the limit of the particle's average x-velocity as the time interval approaches zero: $$v_x = \lim_{\Delta t 	o 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}.$$

Question 2

A dragster moves from $$x_1 = 19$$\ \mathrm{m}$$ at t_1$ = 1.0\ \mathrm{s} to$$ $$x_2 = 277$$\ \mathrm{m}$$ at t_2$ = 4.0\ \mathrm{s}. $$What is its average velocity during this interval?

Accepted Answer

$$86\ \mathrm{m/s}$$

Question 3

On a position vs. time graph, what does the slope of the tangent at a point represent?

Accepted Answer

The instantaneous x-velocity at that point: $$v_x = \frac{dx}{dt}$$

Question 4

A particle moves such that $$\Delta x = 150\ \mathrm{m} in$$ $$\Delta t = 2.0\ \mathrm{s}. $$What is its average velocity during this interval?

Accepted Answer

$$75\ \mathrm{m/s}$$

Question 5

As the time interval $$\Delta t$$ used to calculate average velocity becomes smaller and smaller, what does the average velocity approach?

Accepted Answer

The instantaneous velocity $$v_x$$

Question 6

A ball is thrown from a moving train at an angle of $$55.0^\circ$$ with respect to the horizontal. Which vector equation correctly relates the velocity of the ball relative to the ground ($$\vec{v}_{bg}$$), the velocity of the ball relative to the train ($$\vec{v}_{bt}$$), and the velocity of the train relative to the ground ($$\vec{v}_{tg}$$)?

Accepted Answer

$$\vec{v}_{bg} = \vec{v}_{bt} + \vec{v}_{tg}$$

Question 7

A picture hangs from two strings as shown. If the tension in string 2 ($$T_2) is$$ $$1.7\ \mathrm{N}$$, and the angles are $$65^\circ$$ and $$32^\circ$$, is the tension in string 1 ($$T_1) $$greater than, less than, or equal to $$1.7\ \mathrm{N}$$?

Accepted Answer

Greater than $$1.7\ \mathrm{N}$$

Question 8

Refer to the $$x vs$$. $$t$$ graph with points $$P$$, $$Q$$, $$R$$, and $$S. At $$which point is the instantaneous velocity $$v_x$$ greatest (most positive)?

Accepted Answer

Point P

Question 9

On the same $$x vs$$. $$t$$ graph, at which point is the speed (magnitude of velocity) greatest?

Accepted Answer

Point S

Question 10

On the $$x vs$$. $$t$$ graph, at which point is the acceleration $$a_x$$ greatest (most positive)?

Accepted Answer

Point Q

Question 11

A car travels along a straight road such that its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1. $$What is the instantaneous velocity at $$t = 3\ \mathrm{s}$$?

Accepted Answer

$$v_x = 26\ \mathrm{m/s}$$

Question 12

A particle moves such that $$x(t) = 3t^3$ - 2t^2$ + t. $$What is its acceleration at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$a_x = 28\ \mathrm{m/s^2$}$$

Question 13

A train moves at $$8.35\ \mathrm{m/s}$$ and a passenger throws a ball at $$19.8\ \mathrm{m/s} at$$ $$65.0^\circ$$ relative to the train. What is the horizontal component of the ball's velocity relative to the ground?

Accepted Answer

$$19.8\cos 65.0^\circ + 8.35 = 16.9\ \mathrm{m/s}$$

Question 14

A hockey puck is launched at $$	heta = 15.0^\circ$$ and just clears a $$2.00\ \mathrm{m}$$ high board $$20.2\ \mathrm{m}$$ away. What is the minimum initial speed $$v_0$$ required?

Accepted Answer

$$25.1\ \mathrm{m/s}$$

Question 15

A centrifuge has a radius of $$0.075\ \mathrm{m}$$ and produces a centripetal acceleration of $$52,000g. $$What is the linear speed at the bottom of the test tube?

Accepted Answer

$$200\ \mathrm{m/s}$$

Question 16

A cyclist enters a sandy patch at $$8.4\ \mathrm{m/s}$$ and exits at $$6.4\ \mathrm{m/s}$$ after traveling $$7.2\ \mathrm{m}. $$What is the acceleration in the sandy patch?

Accepted Answer

$$-2.1\ \mathrm{m/s^2$}$$

Question 17

A soccer ball is kicked with an initial speed of $$14.0\ \mathrm{m/s}$$ and after $$0.275\ \mathrm{s}$$ its speed is $$12.9\ \mathrm{m/s}. $$What is the initial direction angle $$	heta$$?

Accepted Answer

$$29.2^\circ$$

Kinematics and Vectors: Foundations of Physics with Calculus

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