Physics.

We know the average velocity is half the sum of the initial and final velocities. However, this question asks us for the initial velocity. Step 1: Rearrange the average velocity formula to solve for the initial velocity. We can solve for the initial velocity by multiplying the average velocity by two and then subtracting the final velocity from the result. vav = (vf + vi) / 2 vav * 2 = [(vf + vi) / 2] * 2 (vav * 2), vf = vf+ vi, vf vi = (vav * 2), vf Step 2: Calculate the magnitude of the initial velocity of the motorcycle. Substitute the following values into our new initial velocity formula: average velocity (vav = 76 m/s), and final velocity (vf = 26 m/s): vi = (vav * 2), vf vi = (76 m/s * 2), 26 m/s vi = 152 m/s, 26 m/s vi = 126 m/s The initial velocity is 126 m/s.

We know that average speed is the distance an object travels divided by the time the object travels. However, this question asks for the distance. Step 1: Rearrange the average speed equation (s = d/t) to solve for distance. s = d/t s * t = (d/t) * t st = d d = st The distance traveled is the average speed of the motorcycle multiplied by the time the motorcycle traveled. Step 2: Convert time from minutes to seconds. Time must be expressed in seconds. So, we need to convert the time the motorcycle travels from minutes to seconds before computing the distance. 2 min * (60 s / 1 min) = 120 s 2 minutes is 120 seconds. Step 3: Calculate the distance traveled. To calculate the distance traveled by the motorcycle, we multiply its average speed (59 m/s) by the new value for time (120 s). d = s * t d = 59 m/s * 120 s d = 7,080 m The motorcycle travels 7,080 m.

Acceleration is the change of velocity over a period of time. Acceleration is represented mathematically by the following equation, where a = acceleration (expressed in m/s2), vf = final velocity (expressed in m/s2), vi = initial velocity (expressed in m/s2), and Δt = change in time (expressed in s). a = (vf, vi ) / Δt Step 1: Convert time from minutes to seconds. We need to express the given values for initial velocity (vi = 45 m/s), its final velocity (vf = 117 m/s), and the new value of the time interval (Δt = 720 s)* into the acceleration formula: a = (vf, vi ) / Δt a = (117 m/s, 45 m/s ) / Δt a = 72 m/s / 720 s a = 0.1 m/s2 The car is accelerating at 0.1 m/s2. *The 720 seconds come from converting the given time of 12 minutes into seconds. Since there are 60 seconds in a minute, you multiply 12 minutes by 60 seconds per minute: 12 minutes×60 seconds/minute=720 seconds12 minutes×60 seconds/minute=720 seconds

Acceleration is the change of velocity over a period of time. Acceleration is represented mathematically by the following equation, where a = acceleration (expressed in m/s2), vf = final velocity (expressed in m/s2 ), vi = initial velocity (expressed in m/s2 ), and Δt = change in time (expressed in s). a = (vf, vi ) / Δt Where a = acceleration, vf = final velocity, vi = initial velocity, and Δt = change in time Step 1: Manipulate the acceleration formula to isolate the variable for time. The change in time can be determined from the acceleration formula as follows: a = (vf, vi ) / Δt a*Δt = [(vf, vi ) / Δt] * Δt aΔt/ a = (vf, vi ) / a Δt = (vf, vi ) / a Step 2: Check the sign of the acceleration. Since the ball uniformly decelerates, the acceleration is negative. Step 3: Calculate the change in time. Substitute the initial velocity (vi = 0.86 m/s), the acceleration ( a = -0.43 m/s2), and the final velocity (vf = 0 m/s) into the new formula for time: Δt = (vf, vi ) / a Δt = (0 m/s, 0.86 m/s ) / -0.43 m/s2 Δt =, 0.86 m/s / -0.43 m/s2 Δt = 2 s It will take 2 s for the ball to come to rest.

The horizontal distance traveled by the toy rocket can be determined using the following formula: dx = vx * t where dx = horizontal distance, vx = horizontal velocity, and t = time. Step 1: Calculate the horizontal velocity of the projectile. We need to know the horizontal velocity to be able to compute the horizontal distance. But the horizontal velocity is not given to us. Instead, we are told that the toy rocket has a velocity of 48 m/s but is launched at an angle (50°), which takes into account the vertical and horizontal velocities. We need to find just the horizontal velocity. To calculate the horizontal velocity, we multiply the initial velocity of the projectile (in this case, 48 m/s) by cosθ: vx = vi * cos θ Where vx = horizontal velocity, vi = initial velocity, and θ = angle above the horizontal We substitute our values into the horizontal velocity equation (vi = 48 m/s; θ = 50°). vx = vi * cos θ vx = 48 m/s * cos (50°) vx = 48 m/s * 0.64 vx = 30.72 m/s Step 2: Calculate the horizontal distance traveled by the toy rocket. Now that we have the horizontal velocity (30.72 m/s), we can plug that value and the value for time (42 s) into the horizontal distance formula: dx = vx * t dx = 30.72 m/s * 42 s dx = 1290 m The toy rocket will travel 1290 m in the horizontal direction. Note: In some of these problems, you will have to round your work along the way (we recommend to the nearest hundredths place) and then choose the closest answer choice. This is how it will be on the HESI exam.

Since the object falls freely, it moves only under the force of gravity. Therefore, its acceleration is equal to the acceleration due to gravity. The height of the balloon is the same as the vertical distance dy that the object falls. The mathematical formula to calculate distance given uniform acceleration is given as follows: dy = (½)gt2 + vi t where dy = vertical distance, g = acceleration due to gravity, t = time, and vi = initial velocity. Step 1: Determine the height of the balloon by calculating the vertical distance traveled by the object. To calculate the vertical distance, substitute the initial velocity (vi = 0 m/s, since the object is dropped), the acceleration (g = 9.8 m/s2, which is the acceleration due to gravity), and the time (t = 80 s). dy = (½)gt2 + vi t vi t cancels out because the initial velocity is 0. dy = (½)gt2 dy = (½) (9.8 m/s2) * (80 s)2 dy = 4.9 m/s2 * 6400 s2 dy = 31,360 m The height of the balloon was 31,360 m when the object was dropped.

The net force acting on the box is simply the sum of all forces acting on the box. Since the two forces are opposing each other, one force is considered positive and the other is considered negative. The net force is represented by the following equation: Fnet = Fleft + (-Fright ) Step 1: Calculate the net force. According to the question, Force to the left, Fleft = 146.5 N Force to the right, Fright = 90.6 N Fleft ＞Fright, and therefore the net force on the box will be towards the left. We plug in the given values to calculate the magnitude of the force: Fnet = Fleft + (-Fright ) Fnet = 146.5 N + (-90.6 N) Fnet= 55.9 N The net force acting on the box is 55.9 N to the left.

Step 1: Calculate the net force. To determine the mass of the object, we must first determine the net force acting on it. According to the question, there are two forces: Force acting to the right, Fright = 432 N Force acting to the left, Fleft = 120 N The forces are acting in opposite directions. The magnitude of the net force can be calculated as: Fnet = Fright + (-Fleft) Fnet = 432 N, 120 N Fnet = 312 N Step 2: Calculate the acceleration using Newton’s second law of motion. Now that the net force (312 N) is determined, we can use Newton’s second law of motion to determine the mass of the box: F = ma Where F=force, k = the constant of proportionality, and a=acceleration First, we convert the formula to solve for mass: F = ma (F/a) = (ma/a) m = (F/a) Substituting the values for net force (312 N) and the acceleration (62 m/s2) of the object: m = (F/a) m = (312 N / 62 m/s2) m = 5.033 kg The mass of the object is 5.03 kg.

Step 1: Rearrange the weight equation to solve for mass. W = mg (W/g) = (mg/g) m = W/g Step 2: Plug in our values for the weight (1300 N) and gravity (9.8 m/s2) to solve for mass: m = (W/g) m = (1300 N / 9.8 m/s2) m = 132.65 kg The mass of the refrigerator is 132.65 kg.

Here, we need to solve for the coefficient of friction. The frictional force (565 N) and the information required to calculate the normal force (72 kg of mass and the acceleration due to gravity, which is 9.8 m/s2) are given to us, so we can manipulate the equation for the frictional force (Ff = μFN) to solve for the coefficient of friction. First, let’s find the normal force. Step 1: Calculate the normal force. The normal force is represented mathematically as: FN = mg Where FN = normal force, m = mass, and g = acceleration due to gravity (9.8 m/s2). The values for mass (72 kg) and gravity (9.8 m/s2) are given to us: FN = (72 kg)*(9.8 m/s2) FN = 705.6 N The normal force is 705.6 N. Step 2: Rearrange the equation for frictional force to solve for the coefficient of friction. Now we rearrange the equation for frictional force (Ff = μFN) to solve for the coefficient of friction: Ff = μFN (Ff / FN) = (μFN / FN) μ = Ff / FN Step 3: Calculate the coefficient of friction. Next, we can plug in our calculated value for normal force (705.6 N) and our given value for the frictional force (565 N) into the frictional force equation to calculate the frictional force: μ = Ff / FN μ = 565 N / 705.6 N μ = 0.8 The coefficient of friction between the box and the surface is 0.8.

Angular acceleration (alpha) = delta-omega / delta-t. Convert times: 5 min = 300 s, 5.5 min = 330 s. alpha = (240 rev/s - 450 rev/s) / (330 s - 300 s) = -210 rev/s / 30 s = -7 rev/s². Convert to rev/min²: multiply by (60 s/min)² = 3600. -7 rev/s² x 3600 = -25,200 rev/min². The original source incorrectly multiplied by 60 instead of 3600. Converting s² to min² requires squaring the conversion factor.

5601.85 N In this question, we use the formula for the centripetal force: F = centripetal force m = mass V = velocity r = radius of the circular path STEP 1. Convert the velocity from km/h to m/s: STEP 2. Fill in the values: F = 5601.85 N

4.7 Use the equation for angular displacement (Θ) to solve this equation. Θ = S / r Where: S = 678 m r = 145 m Solve for the angular displacement: Θ = 678 m / 145 m Θ = 4.7

9.31 Hz. Use the equation frequency = speed / wavelength (derived from the equation speed = frequency × wavelength) Then plugging in the related values: frequency = 67 m/s / 7.2 m frequency = 9.31 Hz.

-18 cm The magnification equation needs to be used, which has the following formula: hi / ho =, di / do Where: hi is the image height ho is the object height do is the object distance di is the image distance. Solve for image height: hi / ho =, di / do hi / 6 cm =, 4.5 cm / 1.5 cm hi / 6 cm =, 3 hi =, 18 cm The negative means the image is inverted.

Like charges repel and opposites attract. When two objects are charged with like (two positive or two negative) charges, they will repel one another. When two objects are charged with opposite charges (one positive and one negative), they will be attracted to one another.

1.5 x 10-13 N To calculate the force between two objects, use the equation for Newton’s Universal Law of Gravitation, which has the form: F = Gm1m2/r2 Where G is the universal gravitational constant (6.67 x 10-11 N m2 kg-2), m1 and m2 are the masses of the two objects, and r is the distance between the objects. Insert the values from the question, and solve for F. F = (6.67 x 10-11 N m2 kg-2)(3.6 kg)(3.5 kg)/(75 m)2 F = 1.5 x 10-13 N

1.5 To calculate this answer, use the following formula: n = c /v, where n is the index of refraction, c is the speed of light in a vacuum (3.00 x 108 m/s), and v is the velocity of light in the medium. n = c /v n = (3.00 x 108 m/s) / 2.0 x 108 m/s n = (3.00 x 108 m/s) / 2.0 x 108 m/s n = 1.5

6.54 Kinetic Energy is the energy an object possesses because of its velocity. Any object that is in motion is using kinetic energy: a child running, a thrown ball, someone skiing down a hill, or a book falling off of a shelf. This is why the equation takes into account the object’s mass and the rate at which they are traveling (their velocity). KE = ½ x mv2 KE = Kinetic energy (expressed in Joules, J) m = mass (expressed in kilograms) v2 = velocity (expressed in meters per second squared) To find the velocity we must isolate it: 2 x KE = 2 x ½ x mv2 2 x KE = mv2 2 x KE / m = mv2 / m 2 x KE / m = v2 m = 70 kg KE = 1500 J v2 = 2 x 1500 J / 70 kg = 42.85 m2/s2 We then take the square root of this and v = 6.54 m/s *Don’t forget that the velocity is squared*

267.2 kg m/s south Since both the cyclist and her bicycle are traveling at 4 m/s, we need to account for the combined mass, which is 66.8 kg. She is riding southward, so the answer needs to include the direction (south) as well. p = momentum (measured in kg⋅m/s) m = mass (measured in kg) v = velocity (measure in m/s) Thus, the momentum, p, is: p = 66.8 kg x 4 m/s p = 267.2 kg m/s south

Gravitational potential energy: PE = mgh. Solve for mass: m = PE / (g * h). PE = 58.6 J, g = 9.8 m/s², h = 1.25 m. m = 58.6 / (9.8 x 1.25) = 58.6 / 12.25 = 4.78 kg. Using g = 9.8 m/s² (the standard value for HESI exam purposes). The answer rounds to 4.78 kg.

2.5 kg m/s The equation for momentum is p = mv. Since the mass of an object remains the same, only its velocity is changed. Thus, the formula for change in momentum is written as Δp = mΔv. The symbol Δ is called “delta” and is used to represent a change in the magnitude (number). In this case, we are using it to represent the change in velocity. Δp = mΔv Δp = (5 kg) (2 m/s, 1.5 m/s) Δp = (5 kg)(0.5 m/s) Δp = 2.5 kg m/s

0.2 A To determine the circuit’s current, use the Ohm’s law equation: V = I × R V = Voltage I = Current R = Resistance Rearranging the equation to solve for I, we get: I = V / R Insert the values into the equation I = 2.4 / 12 I = 0.2 A

Use Coulomb's Law: F = k * |Q1 * Q2| / r². Convert microcoulombs to coulombs (1 uC = 1 x 10^-6 C): +0.5 uC = 5 x 10^-7 C -0.4 uC = 4 x 10^-7 C k = 9 x 10⁹ N.m²/C², r = 2 m. F = (9 x 10⁹) x (5 x 10^-7) x (4 x 10^-7) / (2²) F = (9 x 10⁹) x (20 x 10^-14) / 4 F = (180 x 10^-5) / 4 F = 45 x 10^-5 N. The force is attractive because the charges have opposite signs.

They are a converging lens Convex lenses are also called converging lenses because after light rays pass through them, they converge at a single point called the focal point. Convex lenses are used in magnifying glasses and cameras.