1.An automobile travels on a straight road for 40 km at 30 km/h. It then continues in the same direction for another 40 km at 60 km/h. (a) What is the average velocity of the car during this 80 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed? (c) Graph x vs. t and indicate how the average velocity is found on the graph.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
1.An automobile travels on a straight road for 40 km at 30 km/h. It then continues in the same direction for another 40 km at 60 km/h. (a) What is the average velocity of the car during this 80 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed? (c) Graph x vs. t and indicate how the average velocity is found on the graph.
2.On two different tracks, the winners of the 1 kilometer race ran their races in 2 min, 27.95 s and 2 min, 28.15 s. In order to conclude that the runner with the shorter time was indeed faster, how much longer can the other track be in actual length?
3.An automobile driver on a straight road increases the speed at a constant rate from 25 km/h to 55 km/h in 0.50 min. A bicycle rider on a straight road speeds up at a constant rate from rest to 30 km/h in 0.50 min. Calculate their accelerations.
4. An electric vehicle starts from rest and accelerates at a rate of 2.0 m/s2in a straight line until it reaches a speed of 20 m/s. The vehicle then slows at a constant rate of 1.0 m/s2 until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?
5. The speed of a bullet is measured to be 640 m/s as the bullet emerges from a barrel of length 1.20 m. Assuming constant acceleration, find a) the time that the bullet spends in the barrel after it is fired. b) the acceleration of the bullet.
6. At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s2. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the car be traveling at that instant?
7. If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? How long is it in the air?
8. A pitcher throws a baseball vertically upward with an initial speed of 15.0 m/s, releasing the ball when it is 2.00 m above the ground and then catching it at the same point. What is the maximum height reached by the ball? How long is the ball in the air?
9. A brick is dropped from the roof of a building. The brick strikes the ground in 2.50 s. You may ignore air resistance, so the brick is in free fall. How tall, in meters, is the building? What is the magnitude of the brick’s velocity just before it reaches the ground?
10. A rock is dropped from a treetop 19.6 m high, and then, 1.00 s later, a second rock is thrown down. With what initial velocity must the second rock be thrown if it is to reach the ground at the same time as the first?
11. A projectile is thrown with an initial speed 0=25.0 m/s at an initial angle = 45.00. Find the time T when the projectile is at its maximum height.
12. A tennis ball rolls off the edge of a table top 1.00 m above the floor and strikes the floor at a point 2.80 m horizontally from the edge of the table. Air resistance may be ignored. A) Find the time of flight. B) Find the magnitude of the initial velocity, c) Find the magnitude and direction of the velocity of the ball just before it strikes the floor. Draw a diagram to scale.
13. A physics book slides off a horizontal table top with a speed of 1.25 m/s. it strikes the floor in 0.400 s. Air resistance may be ignored. Find a) the height of the table top above the floor; b) the horizontal distance from the edge of the table to the point where the book strikes the floor; c) the horizontal and vertical components of the book’s velocity and the magnitude and direction of its velocity just before the book reaches the floor.
13. A man throws a football with an initial upward velocity component of 15.0 m/s and a horizontal velocity component of 25.0 m/s. Air resistance may be ignored. A) How much time is required for the football to reach the highest point of the trajectory? B) How high is this point? C) How much time (after being thrown) is required for the football to return to its original level? How does this compare with the time calculated in part(a)? d) How far has it travelled horizontally during this time?
14. A Civil War mortar called the Dictator fired its 90.7-kg (200-lb) shell a maximum horizontal distance of 4345 m (4752 yd) when the shell was projected at an angle 450above the horizontal. Air resistance may be ignored. A) What was the muzzle speed of the shell( the speed of the shell as it left the barrel of the mortar)? B) What maximum height above the ground did the shell reach? C) For what amount of time was the shell in the air?
15. A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center. The linear speed of a passenger on the rim is constant and equal to 8.00 m/s. a) What are the magnitude and direction of the passenger’s acceleration as she passes through the lowest point in her circular motion? B) How much time does it take the Ferris wheel to make one revolution?
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