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2. The resistance to motion of a particle in air is approximately proportional to the square of its velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression a =- kv', where k is taken to be a constant whose numerical value depends on the prevailing air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m", in what distance and elapsed time after firing will the velocity be reduced to 8m/s?

2. The resistance to motion of a particle in air is approximately proportional to the square of its velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression a =- kv', where k is taken to be a constant whose numerical value depends on the prevailing air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m", in what distance and elapsed time after firing will the velocity be reduced to 8m/s?

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1. A particle moves along a straight line so that after t seconds its displacement s in meters from a fixed reference point O on the line is given by: s =- 4 + 302 – 48t + 12. The particle is 4m to the left of the origin at t= 25. Determine a. The acceleration of the particle when t=35 b. The displacement during the interval from t=2s to t=5s c. The total distance traveled during the interval from t=2s to t=5s d. The average velocity during the interval from t=2s to t=55 2. The resistance to motion of a particle in air is approximately proportional to the square of its velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression a =- ku', where k is taken to be a constant whose numerical value depends on the prevailing air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m*, in what distance and elapsed time after firing will the velocity be reduced to 8m/s? 3. The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2 and t is in seconds. When t-0, the acceleration of the particle is 4 m/s^2 to the left. During the interval from t=2 to t=45, the displacement of the particle is 20 m to the right. Determine: a. The initial velocity of the particle b. The velocity of the particle at the end of the displacement period c. The position of the particle when t=3s 4. An average car can decelerate at the maximum rate of 8m/s^2 on the highway. Find the total emergency stopping distance measured from the point where the driver first sights the danger for a car traveling at a speed of 108km/hr. The reaction time for a good driver is about % of a second from the instant he sights the danger until he actually applies the brakes. 5. A stone is dropped from a balloon which rises vertically at a constant rate for 4 seconds from the ground. The stone reaches the ground in 10 seconds. Find the velocity and height of the balloon when the stone is dropped.
Transcribed Image Text:1. A particle moves along a straight line so that after t seconds its displacement s in meters from a fixed reference point O on the line is given by: s =- 4 + 302 – 48t + 12. The particle is 4m to the left of the origin at t= 25. Determine a. The acceleration of the particle when t=35 b. The displacement during the interval from t=2s to t=5s c. The total distance traveled during the interval from t=2s to t=5s d. The average velocity during the interval from t=2s to t=55 2. The resistance to motion of a particle in air is approximately proportional to the square of its velocity v for speeds not exceeding 150 m/s. Thus, the deceleration is given by the expression a =- ku', where k is taken to be a constant whose numerical value depends on the prevailing air conditions and the shape, roughness, and mass. If a particle which moves in a horizontal straight line is fired with an initial velocity of 50 m/s for a condition where k-1/100m*, in what distance and elapsed time after firing will the velocity be reduced to 8m/s? 3. The rectilinear motion of a particle is governed by the equation a = 6t – 4 where a is in m/s^2 and t is in seconds. When t-0, the acceleration of the particle is 4 m/s^2 to the left. During the interval from t=2 to t=45, the displacement of the particle is 20 m to the right. Determine: a. The initial velocity of the particle b. The velocity of the particle at the end of the displacement period c. The position of the particle when t=3s 4. An average car can decelerate at the maximum rate of 8m/s^2 on the highway. Find the total emergency stopping distance measured from the point where the driver first sights the danger for a car traveling at a speed of 108km/hr. The reaction time for a good driver is about % of a second from the instant he sights the danger until he actually applies the brakes. 5. A stone is dropped from a balloon which rises vertically at a constant rate for 4 seconds from the ground. The stone reaches the ground in 10 seconds. Find the velocity and height of the balloon when the stone is dropped.
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