university physic 1

Question

1) If the displacement of an object is related to time according to the expression x=B.t^2, find the dimensions of the “B”. (2 PUAN)

2) Suppose your hair grows at the rate of 1/30 inch per day. Find the rate at which it grows in nanometers per second. (2 PUAN)

3) The base of a pyramid covers an area of 13.0 acres (1 acre = 43560 ft2) and has a height of 481 ft. If the volume of a pyramid is given by the expression V=ab/3, where “a” is the area of the base and “b” is the height, find the volume of this pyramid in cubic meters. (2 PUAN)

4) The radius of the planet Saturn is 585107 m, and its mass is 5681026 kg. By considering these information, find the density of Saturn (its mass divided by its volume) in grams per cubic centimeter (The volume of a sphere is given by 4/3 r^3) (2 PUAN).

5) The micrometer (1 pm) is often called the micron. By considering this information, find how many microns make up 5.0 km (2 PUAN)

6) A gry is an old English measure for length, defined as 1/10 of a line, where line is another old English measure for length, defined as 1/12 inch. A common measure for length in the publishing business is a point, defined as 1/12 inch. What is an area of 3.0 gry2 in points squared (points2) ?

(2 PUAN)

7) Gold, which is a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (4 PUAN)

A) If a sample of gold, with a mass of 27.63 g, is pressed into a leaf of 2.0 m thickness, what is the area of the leaf ?

B) If, instead, the gold is drawn out into a cylindrical fiber of radius 3 m, what is the length of the fiber?

8) By assuming that water has a density of exactly 1 g/cm3, find the mass of one cubic meter of water in kilograms. (2 PUAN)

9) Iron has a density of 7.87 g/cm3, and the mass of an iron atom is 9.27 x 10-26 kg. If the atoms are spherical and tightly packed, find the volume of an iron atom. (2 PUAN)

10) A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30o east of north for 25 km. Considering the given data, determine the magnitude and the angle of the car's total displacement from its starting point. (3 PUAN)

11) For the vectors A ⃗=(3.0m).i ⃗+(4.0m).j ⃗ and B ⃗=(5.0m).i ⃗+(-2.0m).j ⃗, find the results of the vector operations given below; (4 PUAN)

A) C ⃗=A ⃗-2B ⃗ ; find the vector C ⃗ and its magnitude.

B) Find the angle between the vector C ⃗ and the unit vector j ⃗.

12) Two vectors are given by A ⃗=(4.0m).i ⃗-(3.0m).j ⃗+(1.0m).k ⃗ and B ⃗=(-1.0m).i ⃗+(1.0m).j ⃗+(4.0m).k ⃗. By considering the equation A ⃗-B ⃗+C ⃗=-2i ⃗+j ⃗-k ⃗, find the vector C ⃗ in unit vector notation. (2 PUAN)

13) In the sum A ⃗+B ⃗=C ⃗, vector A ⃗ has a magnitude of 12.0 m and is angled 60.0o counterclockwise from the +x direction, and vector C ⃗ has a magnitude of 15.0 m and is angled 30.0o counterclockwise from the -x direction. Considering the given information, find the magnitude of the vector B ⃗ and the angle between this vector and the unit vector i ⃗ ? (3 PUAN)

14) A vector A ⃗ of magnitude 10 units and another vector B ⃗ of magnitude 6.0 units differ in directions by 60o. Find the scalar product of the two vectors and the magnitude of the vector product A ⃗ x B ⃗. (4 PUAN)

15) A particle moves according to the equation x(t)=5t^2, where x(t) is in meters and t is in seconds. Considering the given data, find the corresponding average velocity value for the time interval 2.00 s - 5.00 s. (2 PUAN).

16) The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration of 25.60 m/s2 for 4.20 s, making straight skid marks 62.4 m long, all the way to the tree. With what speed does the car then strike the tree ? (3 PUAN)

17) The brakes on your car can slow you at a rate of 5.2 m/s2. If you are going 150 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 80 km/h speed limit ? (2 PUAN)

18) An electric vehicle starts from rest and accelerates at a rate of 4.0 m/s2 in a straight line until it reaches a speed of 30 m/s. The vehicle then slows at a constant rate of 2.0 m/s2 until it stops.

(4 PUAN)

A) How much time elapses from start to stop ?

B) How far does the vehicle travel from start to stop ?

19) On a dry road, a car with good tires may be able to brake with a constant deceleration of 5.0 m/s2.

(4 PUAN)

A) How long does such a car, initially traveling at 30.5 m/s, take to stop?

B) How far does it travel in this time?

20) A ball is thrown directly downward with an initial speed of 6.00 m/s from a height of 35.0 m. After what time interval does it strike the ground ? (2 PUAN)

21) A motorist drives along a straight road at a constant speed of 20.0 m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 2.00 m/s2 to overtake her. Assuming that the officer maintains this acceleration, 

A) determine the time interval required for the police officer to reach the motorist.

B) find the speed and the total displacement of the officer as he overtakes the motorist.

(4 PUAN)

22) A hot-air balloon is ascending at the rate of 12 m/s and is 80 m above the ground when a package is dropped over the side. (4 PUAN)

A) How long does the package take to reach the ground?

B) With what speed does it hit the ground ?

23) A rock is thrown vertically upward from ground level at time t=0s. At t=1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. What is the height of the tower ? (3 PUAN)

24) A hoodlum throws a stone vertically downward with an initial speed of 12.0 m/s from the roof of a building, 30.0 m above the ground. (4 PUAN)

A) How long does it take the stone to reach the ground ?

B) What is the speed of the stone at impact?

25) An ion's position vector is initially r ⃗=(5i ⃗-6j ⃗+2k ⃗)m, and 10 s later it is r ⃗=(-2i ⃗+8j ⃗-2k ⃗)m. In unit-vector notation, what is its v ⃗_avg during the 10 s ? (2 PUAN)

26) An electron's position is given by r ⃗=(3ti ⃗+4t^2 j ⃗+2k ⃗) with “t” in seconds and r ⃗ in meters.

(6 PUAN)

A) Determine the electron's velocity v ⃗(t) in unit vector notation. 

B) What is the magnitude of v ⃗(t) at t=2.00 s ?

C) What is the angle between v ⃗(t) and the unit vector i ⃗ ?

27) The velocity v ⃗ of a particle moving in the xy plane is given by v ⃗=(6t-4t^2 ) i ⃗+8j ⃗, with v ⃗ in meters per second and “t” in seconds. (6 PUAN)

A) What is the acceleration when t=3s ?

B) When (if ever) is the acceleration zero ?

C) When (if ever) is the velocity zero ?

28) A proton initially has the velocity v ⃗=4i ⃗-2j ⃗+3k ⃗ and then 4s later has the velocity v ⃗=-2i ⃗-2j ⃗+5k ⃗ (in meters per second). For that 4.0 s find the following quantities (6 PUAN)

A) the proton's average acceleration a ⃗_avg in unit-vector notation

B) the magnitude of a ⃗_avg

C) the angle between a ⃗_avg and the positive direction of the x axis

29) A ball is thrown toward a wall at speed 25m/s and at angle =〖40〗^o above the horizontal axis. The wall is at a distance (d=22m) from the release point of the ball. (6 PUAN)

A) How far above the release point does the ball hit the wall ?

B) What are the horizontal and vertical components of its velocity as it hits the wall?

C) When it hits, has it passed the highest point on its trajectory ?

30) A fish swimming in a horizontal plane has velocity v ⃗_i=(4i ⃗+j ⃗ )m/s at a point in the ocean where the position relative to a certain rock is r ⃗_i=10i ⃗-4j ⃗ m. After the fish swims with constant acceleration for 20.0 s, its velocity is v ⃗_f=(20i ⃗-5j ⃗ )m/s. (6 PUAN)

A) What are the components of the acceleration of the fish ?

B) What is the direction of its acceleration with respect to unit vector i ⃗ ?

C) If the fish maintains constant acceleration, where is it at t =25.0 s and in what direction is it moving?

Answer 1

Hello Veli,

Please try some of these out on your own. I'd be glad to help you through the ones that you're having difficulty with.