Given the equation: a = kr"vm where a is the acceleration of a particle moving with speed v in a circle of radius r, and k is a constant. By using dimensional analysis prove this equation to determine values of n and m, then write the simplest form of an equation for the acceleration.

Q: Police use the formula: V20L to estimate the speed of a car, v, in miles per hour, based on the…

A: Given: The Length of skid mark L = 158 ft. The velocity formula is given as, v=20L

Q: The instantaneous speed of a particle moving along one straight line is v(t) = ate"2t where the…

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Q: The position of a certain particle moving along the x axis is determined from the expression  x(t)…

A: Given expression ,                                  x(t) = btu + ctv  Where , x is in meters when t…

Q: Light travels at a speed of about 3.0 x 108 m/s. (a) How many miles does a pulse of light travel in…

A: Given value--- speed of light = 3 × 108 m/s. time = 0.1 sec  We have to find--- (a) How many…

Q: (a) determine the average distance between the Earth and the Sun. Then calculate the average speed…

A: The average distance between the Sun and the Earth is given as, r=1.496×108 km The time taken by the…

Q: A particle moves along the h-axis (dimension of length) so that: h = t3 - 3t2 - 45t (in feet, where…

A: the equation of particle along the h-axis is given by h(t) = t3 - 3t2 -45t  ------- (1) to determine…

Q: 1) A 2-kg block bar is attached to a 5-kg uniform cylinder by a square pin, P, as shown. Assuming…

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Q: Time, t (s) Velocity, v (m/s) 4 12 8 42 10 55 The velocity over the time interval 4 s ts 10 is…

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Q: Hardy, an avid TikToker, decided to look at his wristwatch to tell his friend dolphins the current…

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Q: what is the dimension of A in terms of [L], [M], and [T]?

A: Given data: The acceleration is: a The length is: L meter The mass is: M kg The time is: T sec The…

Q: Alishba wakes up late and runs to school, covering a distance of 2.55 km in a direction of [N200 E]…

A: Alishba runs to school, covering a distance of 2.55 km in a direction of [N200 E].She then goes to…

Q: Suppose your hair grows at the rate 1/31 in. per day. Find the rate at which it grows in nanometers…

A: Given data:  Hair growth rate = 1/31 in. per day Required: Hair growth rate in nm/s

Q: our car speedometer has an uncertainty of 4.8 km/h at a speed of 95 km/h. What is the percent…

A: speed of car= 95 km/hr Uncertainity = 4.8 km/hr

Q: The position of a moving particle in vortex is expressed as, x(t) = x0 sin(a√t + bt^2) where x0 is…

A: An equation holds correct if the dimensions of the quantities involved in both sides of the equation…

Q: “An object is moving at a speed of v(t)= 3(t^2-1)+5tan (7t), where V is in m / s and t in seconds.…

A: Given  V(t) = 3t2 -3 +5tan(7t)  The acceleration si A(t) = ????

Q: PROBLE A surveyor walks as shown in the figure then due south for 10.0km. What is his total…

A: Q 1) The ratio of distance moved is South and East is 2:3. Let them be 2x towards south and 3x…

Q: er robbing a bank in Dodge City, a robber gallops off at 14 m(i)/(h). 10 minutes later, the marshall…

A: Speed of Robber,                             Speed of marshall.                             The time…

Q: Acceleration is related to velocity and time by the followingexpression: a = vptq. Find the powers p…

A: Acceleration of a particle is related to velocity and time as- We have to determine the values of p…

Q: Using the answers from Question 1(a), determine the solutions of the equation (x+1)* = 16(x–1)*…

A: The given equation is: x+14=16x-14 Now, solving the above equation as:…

Q: If you make multiple measurements of your height, you are likely to find that the results vary by…

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Q: A car speedometer has a 5% uncertainty. What is the range of possible speeds (in km/h) when it reads…

A: Given:-  The uncertainty of the speedometer of the car is 5 %  The speed of car read by the…

Q: Suppose we are told that the acceleration (a) of a particle moving with uniform speed (v) in a…

A: Given  a particle moving in circle of radius (r) with uniform speed  acceleration(a)=krnvm

Q: The position of a particle moving along the x axis may be determined from the expression x(t) = btu…

A: Given expression: xt=btu+ctv

Q: A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed…

A: (a)Co-ordinates of stone’s initial position is,

Q: find the area velocity of a particle moving along the path r= a cos w t i + b sin w t j, where a, b…

A: The area velocity is given by  dA⇀dt=r⇀×dr⇀dt2 given that r⇀=acosωti^+bsinωtj^…

Q: This explanation is very confusing.  Can you be so kind and detail the steps and math calculations.…

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Q: The following data for the instantaneous velocity, v, versus time, t, was obtained to fit he…

A: The given set of data is: Time (t) Velocity (v) 0.2 0.332 0.4 0.508 0.6 0.645 0.8 0.798…

Q: A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly is…

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Q: After an​ accident, police can estimate the speed that a car was traveling by measuring its skid…

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Q: After Dan makes a basket, Josephine claims she can find the amount of time the ball was in the air…

A: It is only the height that is provided to solve this problem. So, we can only use height in this…

Q: A person travels by car from one city to another with different constant speeds between pairs of…

A: Determine the distance traveled when the speed is 70 km/h. Determine the distance traveled when the…

Q: Solve M„VN at (1,1-1) When M = (2yz)i – (x²y)j+(xz²)k and N = 2x?yz3

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Q: given that A+2B = x1j +y1j and 2A-B = x2i + y2j what is A?

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Q: Problem 1-17 Using the base units of the SI system, show that F = G(m,m¿)/r² is a dimensionally…

A: The equation of F can be given as, Here, m1 denotes the mass of the first object (in kg), m2…

Q: When traveling from point (B) to point (D), what is the total distance traveled by Car B_2? Report…

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Q: a) What is the average speed in kilometers per second of the Earth around the sun, given that the…

A: Radius of the earths orbit, r=1.5×108 kmThe distance covered by the earth in one complete revolution…

Q: The motion of a particle is given by a = 6v1/3, where a is in feet per sec² and v in feet per sec.…

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Q: The position of a moving particle in vortex is expressed as, x(t) = xo sin(at³ + bt3/2) where xo is…

A: Given displacement equation: xt=x0sinat3+bt32 Now, the term at3+bt32 is dimensionless as it is only…