Question

Solve exactly if possible. Express all decimals to 4 significant figures. 1) 2) 3) 4) 5) 6) 7) What are Newton's Laws of motion? What is a "frame of reference"? What is a coordinate system? Express the point x-3, y-4 using polar coordinates. What is the SI unit for force? How is it defined using SI base units? What are the four fundamental forces in the universe? What is the approximate gravitational acceleration, g, near the Earth's surface? If this value varies by 0.7% around the world, what is the range of values for g? A plane flies 80 miles due west and then 120 miles due east. What is the distance traveled and what is the displacement for the trip? 8) A particle initially at rest accelerates at 5.0 m/s2. How fast is it moving after 3.2 s? How far will it travel in 4.0 s? How long will it take to travel 100.0 m? 9) A caris moving at 12.0 m/s and then accelerates at 1.5 m/s2 for 10 seconds. What is the velocity after 10 seconds? How far did the car travel during this time? 10) A ball is dropped from height Hand accelerates downward with acceleration g. In terms of H and g, solve for the time it takes to hit the ground. 11) A rock is thrown straight up in the air at 6.2 m/s and it is released 1.8 m above the ground. Write an equation of motion to describe the height of the rock relative to the ground. (neglect air resistance and use g- 9.8 m/s2) 12) A sprinter running a 100 m race starts at rest and accelerates at constant acceleration A for 3.0 seconds and then maintains a constant velocity. In terms of A, what is the position of the runner after 3.0 seconds? What is A if the sprinter finishes the race in 12.0 seconds? 13) What force is needed to accelerate a 30.0 lb block at 2.2 m/s2 14) What force is needed to stop a 1500 kg car in 40 m if it is initially moving at 35 miles per hour? 15) A particle is moving in a straight line with constant acceleration a. Derive a general equation for velocity v at position x in terms of initial velocity vo, initial position xo, and acceleration a. 16) You are in the left lane (speeding) at 40 m/s when you notice a police car ahead of you traveling at 30 m/s (the speed limit). When you are 45 m apart you start decelerating at 1.0 m/s2. Will you pass the police car and get a ticket? 17) A car is traveling at 25.0 m/s approaching a bicyclist moving at 7.0 m/s in the same direction. There is 75 m between them when the driver hits the brakes. What is the deceleration needed to avoid a collision?

Answer 1

(1) Sir Issac Newton gives three laws of motion -

(i) Newton's first law of motion - An object will remain in rest or in the state of uniform motion in the state line unless acted upon by an external force. It may be seen as a statement about inertia, that object will remain in their state of motion unless a force acts to change the motion.

(ii) Newton's second law of motion - The acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction, and inversely proportional to the mass of the object.

(iii) Newton's third law of motion - For every external force that acts on an object there is a force of equal magnitude but opposite in direction which acts back on the object which exerted that external force.

(2) Frame of reference -

To analyse the motion of a body, first we need to find the location of the body at a certain instant of time. To do this we have the coordinate system. The system of X, Y and Z axes, which are perpendicular to each other, are used to mark the position of an object in three dimensional space. This frame of three-axes is the frame of reference, which originates from the interaction of the three axes which is the origin.

(3) Coordinate system -

A coordinate system is a method for identifying the location of a point on the earth. Most coordinate systems use two numbers, a coordinate, to identify the location of a point. Each of these number indicates the distance between the point and some fixed reference point, called origin. The first number is known as X value and the second number is known as Y value.

X = 3, Y = 4

magnitude, R = sqrt[X^2 + Y^2] = sqrt[3^2 + 5^2] = 5

$\Theta$ = tan^-1(Y/X) = tan^-1(4/3) = 53.1 deg

So, in polar form, the value = R$\angle \Theta$ = 5$\angle 53.1$ deg