Question 1

A car accelerates uniformly from rest and covers a distance of $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$a = 8\ \mathrm{m/s^2$}$$

Question 2

A projectile is launched with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$v_{iy} = 20 \sin 30^\circ = 10\ \mathrm{m/s}$$

Question 3

A block slides up a $$30^\circ$$ incline with an initial speed of $$10\ \mathrm{m/s}. $$The coefficient of kinetic friction is $$0.1. $$How far up the incline does the block travel before stopping? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta x = 8.6\ \mathrm{m}$$

Question 4

A drone flies horizontally at $$4\ \mathrm{m/s}$$, $$10\ \mathrm{m}$$ above the ground, and is $$20\ \mathrm{m}$$ away from you. If you throw a rock straight up so that it lands on the drone, what initial speed must you give the rock? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_{iy} = 26.5\ \mathrm{m/s}$$

Question 5

A plane is flying horizontally at $$30\ \mathrm{m/s}$$, $$100\ \mathrm{m}$$ above the ground. How far from a target should a package be released to land on the target? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta x = 135\ \mathrm{m}$$

Question 6

A particle moves with velocity $$v_x(t) = 2t^2$ - 4t. $$What is the acceleration at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$a_x = 4\ \mathrm{m/s^2$}$$

Question 7

A block of mass $$m$$ slides down a frictionless incline of angle $$	heta. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta$$

Question 8

A $$2\ \mathrm{kg}$$ object is acted on by a net force of $$10\ \mathrm{N} in $$the $$x-$$direction and $$6\ \mathrm{N} in $$the $$y-$$direction. What is the magnitude of its acceleration?

Accepted Answer

$$a = 5.83\ \mathrm{m/s^2$}$$

Question 9

A car travels at a constant velocity of $$20\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is the displacement during this time?

Accepted Answer

$$\Delta x = 200\ \mathrm{m}$$

Question 10

A $$5\ \mathrm{kg}$$ box is pulled across a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.2. $$What is the frictional force acting on the box? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_{k} = 9.8\ \mathrm{N}$$

Question 11

A ball is thrown vertically upward with an initial velocity $$v_{iy}. $$Which equation gives the time to reach maximum height?

Accepted Answer

$$t = \frac{v_{iy}}{g}$$

Question 12

A $$1\ \mathrm{kg}$$ object falls through air and experiences a drag force $$F_{drag} = \frac{1}{2} c \rho A v^2$. If c = 0.5$, $$\rho = 1.2\ \mathrm{$$kg/m^3$$}$$, A = 0.1$$\ \mathrm{$$m^2$$}$$, and v = 10$$\ \mathrm{m/s}$$, what is the drag force?

Accepted Answer

$$F_{drag} = 3\ \mathrm{N}$$

Question 13

A block is at rest on a horizontal surface. The coefficient of static friction is $$0.4. $$What is the maximum force that can be applied before the block starts to move? (Assume $$m = 2\ \mathrm{kg}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_{max} = 7.84\ \mathrm{N}$$

Question 14

A car accelerates from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a = 4\ \mathrm{m/s^2$}$$

Question 15

A ball is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = 3.03\ \mathrm{s}$$

Question 16

A $$3\ \mathrm{kg}$$ object is acted on by two forces: $$F_1 = 6$$\ \mathrm{N}$$ east and F_2$ = 8\ \mathrm{N}$$ north. What is the magnitude of the object's acceleration?

Accepted Answer

$$a = 3.33\ \mathrm{m/s^2$}$$

Question 17

A car moves with constant acceleration. Which equation relates the final velocity, initial velocity, acceleration, and displacement?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2a\Delta x$$

Question 18

A $$10\ \mathrm{kg}$$ box is at rest on a ramp inclined at $$25^\circ. $$What is the normal force acting on the box? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_N = 88.8\ \mathrm{N}$$

Question 19

A train moves with a velocity given by $$v(t) = 3t^2$ - 2t. $$What is the total displacement after $$2\ \mathrm{s}$$, starting from rest?

Accepted Answer

$$\Delta x = 6\ \mathrm{m}$$

Kinematics and Dynamics: Study Notes for College Physics

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