# Physics: Density, Vectors, Speed, Acceleration, Velocity

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1.7. Which of the following equations are dimensionally correct? (a) vf = vi + ax

(b) y = (2 m)cos(kx), where k = 2 m-1.

1.26. The radius of a solid sphere is measured to be (6.50 ± 0.20) cm, and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

1. 44. Vector has x and y components of -8.70 cm and 15.0 cm, respectively; vector has x and y components of 13.2 cm and -6.60 cm, respectively. If, what are the components of ?

2. 12. An object moves along the x axis according to the equation x(t) = (3.00t2 - 2.00t + 3.00) m, where t is in seconds. Determine (a) the average speed between t = 2.00 s and t = 3.00 s, (b) the instantaneous speed at t = 2.00 s and at t = 3.00 s, (c) the average acceleration between t = 2.00 s and t = 3.00 s, and (d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s.

2. 25. A truck on a straight road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 20.0 m/s. Then the truck travels for 20.0 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00 s. (a) How long is the truck in motion? (b) What is the average velocity of the truck for the motion described?

2. 55. A rock is dropped from rest into a well. The sound of the splash is heard 2.40 s after the rock is released from rest. How far below the top of the well is the surface of the water? The speed of sound in air (at the ambient temperature) is 336 m/s.

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1.7. Which of the following equations are dimensionally correct? (a) vf = vi + ax

(b) y = (2 m)cos(kx), where k = 2 m-1.

Solution: a) vf = vi + ax

Dimensions of the left hand side: vf (velocity) - L1T-1

Dimensions of the right hand side: vi (velocity) - L1T-1

a (acceleration) - L1T-2

x (displacement) - L1T0

ax - L2T-2

As the dimensions of the two terms on the right hand side are different, the equation is dimensionally incorrect.

(b) y = (2 m)cos(kx), where k = 2 m-1

Dimensions of the left hand side: y (displacement) - L1T0

Dimensions of the right hand side: kx - [L-1T0][ L1T0] = L0T0 (kx is dimensionless)

2m - L1T0

Dimensions of both the sides being same, the equation is correct.

1.26. The radius of a solid sphere is measured to be (6.50 ± 0.20) cm, and its mass is measured to be (1.85 ± 0.02) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.

Solution: In case of multiplication or division of quantities with errors, the resultant quantity has a relative (or percentage) error which is the sum of the relative errors in the quantities being multiplied or divided.

Radius of the solid sphere = R = (6.50 ± 0.20) cm

% error in the radius value = (0.20/6.50) x 100 = 3.07%

Volume of the sphere = V = (4/3) ПR3

As the calculation of volume involves multiplication of the radius R thrice, the error in the volume is 3 x 3.07 = 9.21%

Hence, volume of the sphere V = ...

#### Solution Summary

The solution determines the density, vectors, speed, acceleration and velocity.

Physics: velocity, speed, force, temperature, energy, magnitude, acceleration, wave

1) A particle moves according to the equation x=10t2, where x is in meters and t is in seconds. Find the average velocity for the time interval from 2.0 second to 2.1 second.

A) 41 m/s

B) 100 m/s

2) If A = (12i -16j) and B = (-24i + 10j), what is the magnitude of the vector C = (2A - B)?

A) 42

B) 22

C) 64

D) 90

3) A room measures 3.0 m by 4.5 m by 6.0 m. The heating and air conditioning ducts to and from the room are circular with diameter 0.30 m, and the air in the room is to be exchanged every 12 minutes. What is the necessary flow speed in the duct? (Assume that the density of the air is constant)

A) 0.6 m/s

B) 1.6 m/s

C) 3.2 m/s

D) 4.1 m/s

5) A 50-kg ice skater is moving at 5 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 1 m around the pole. Determine the force exerted by the rope on her arms.

A) 1250 N

B) 250 N

C) 50 N

D) 1100 N

6) Steam at 1000C is added to ice at O0C. The mass of the steam is 10.0 g and the mass of the ice is 50.0 g. What is the final temperature of the mixture?

A) 20.4oC

B) 40.4oC

C) 80.8oC

D) 90.1oC

7) The speed of a 4.0-kg object is given by v = (2t) m/s, where t is in seconds. At what rate is the resultant force on this object doing work at t = 1 second?

A) 48 W

B) 40 W

C) 56 W

D) 16 W

8) A 10-kg object is initially at the top of a rise, at point A. It then moves down to point B. Choose point B to be the zero level for gravitational potential energy. Find the change in potential energy of the object if point B is 10 m lower than point A.

A) - 980

B) - 10

C) - 100

D) - 98

9) A 3-kg particle has a velocity of (3i - 4j) m/s. Find the magnitude of its momentum.

A) 9 kg.m/s

B) -12 kg.m/s

C) 15 kg.m/s

D) 3 kg.m/s

10) At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2 rad/s. Two seconds later it has turned 5 complete revolutions. What is the angular acceleration of this wheel?

A) 17 rad/s^2

B) 14 rad/s^2

C) 20 rad/s^2

D) 23 rad/s^2

11) A car of mass 1000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg.m^2/s) relative to the center of the racetrack?

A) 5 x 10^2

B) 5 x 10^6

C) 2.5 x 10^6

D) 2.5 x 10^4

14) How many significant figures are in the following number? 0.0064

A) 2

B) 3

C) 4

D) 5

15) In order to understand the concept of temperature it is useful to understand

A) the zeroth law of thermodynamics

B) the first law of thermodynamics

C) the second law of thermodynamics

D) none of the above

16) An archer shoots an arrow with a velocity of 45 m/s at an angle of 50 degrees with the horizontal. What is the height of the arrow at a point 150 meters downrange?

A) 4.7 m

B) 47.0 m

C) 5.6 m

D) 56.0 m

17) A sinusoidal wave is described by y=(0.30 m)sin(0.20x-40t ). Determine the wave speed.

A) 100 m/s

B) 133 m/s

C) 150 m/s

D) 200 m/s

18) The exhaust temperature of a Carnot heat engine is 350oC. What is the intake temperature if the efficiency is 25.0%?

A) 400oC

B) 543oC.

C) 558oC

D) 830oC

20) A house has well-insulated walls. It contains a volume of 100 m3 of air at 300 K. Calculate the energy required to increase the temperature of this diatomic gas by 2oC. Assume it is heating at constant pressure and use Cp=7R/2.

A) 118 kJ

B) 236 kJ

C) 354 kJ

D) 472 K

21) If the speed at some point in a fluid changes with time, the fluid flow is not __________.

A) steady

B) irrotational

C) incompressible

D) nonviscous

22) A bowling ball rolls without slipping on a flat surface. The ball has ___________.

A) rotational kinetic energy

B) translational kinetic energy

C) both a and b

D) neither a or b

23) In uniform circular motion, there is a ____________.

A) constant velocity

B) constant angular velocity

C) zero acceleration

D) net tangential acceleration

24) Linear momentum is ____________.

A) always conserved

B) a scalar quantity

C) a vector quantity

D) unrelated to force

25) If the net force on an object is zero, the object must _______________.

A) be at rest

B) be in motion with constant velocity

C) have zero acceleration

D) none of these