Presentation on theme: "3-instvelacc Review Three cars are starting on a 30-mile trip. They start at the same time, and arrive ½ hour later. Slow start, then becoming faster Fast."— Presentation transcript:
13-instvelaccReviewThree cars are starting on a 30-mile trip. They start at the same time, and arrive ½ hour later.Slow start, then becoming fasterFast start, then becoming slowerConstant speedWhich car has the highest average speed?Draw the x-t graph for the three cars.Draw the v-t graph for the three cars.
2Reading assignment 2.2Which of the following statements about the instantaneous velocity is false?The inst. Velocity is equal to the slope of the tangent in an x-t graph.The instantaneous velocity is equal to the speed at any time.The instantaneous velocity is the derivative of position with respect to time.The inst. Velocity can be written as
3Reading Assignment 2.3: B. A. C. D. The slope of which of these green lines could be used to find the average acceleration of a particle?vxtxtB.A.vxtvxtC.D.
4Reading Assignment: A. B. C. D. Which of the following is a correct equation for the instantaneous acceleration in x direction?A.B.C.D.
5Instantaneous velocity Constant speed:straight line in x-t graphSlope = velocity = average velocityWhat happensif the velocity isnot constant?
6Instantaneous velocity The sled becomes faster as it goes downhill.Which of the following curves does best represent position versus timefor the sled?BxCDAt
7Instantaneous velocity The sled becomes faster as it goes downhill.Which of the following curves does best represent position versus timefor the sled?xCt
8Instantaneous velocity x(t) position x is a function of time txx2x1tt1t2velocity at time t1 ?
9Instantaneous velocity xx3x1tt1t3t2velocity at time t1 ?
10Instantaneous velocity xx4x1tt1t4t3t2velocity at time t1 ?
11Instantaneous velocity xtt1velocity at time t1 ?
13Instantaneous velocity is the first derivative of distance with respect to timeSlope in x-t graphUnit of measurement: 1 m/sSpeed is the magnitude of the instantaneous velocity
14Instantaneous velocity - example A robot is logging its position as a function of time, given below. Sketch the graph of velocity versus t.Position xTime tt1t2
15A ball is rolling up an inclined straight length of track A ball is rolling up an inclined straight length of track. Its distance from the bottom of the track is described by the equationFind an expression for the velocity as a function of time.Where was the ball when the clock read zero?Where is the highest x-position the ball can reach?Find the acceleration of the ball as a function of time.At which time does the ball fall off the bottom end of the track?Sketch the x-t graph, the v-t graph, and the a-t graph.
16Sketch a-t and x-t graphs. You may have noticed while driving your car’s velocity does not continue to increase, even though you keep your foot on the gas pedal (drag, friction, engine efficiency). Shown is a v-t graph of a typical car starting from rest.vtSketch a-t and x-t graphs.
17Example: 1-d acceleration A school bus is approaching a stop and slowing down from 15 mph to zero. This takes 4.5 seconds. Determine the average acceleration of the school bus.After the stop the school bus resumes its trip by reaching 15 mph after 6 seconds. Find the average acceleration.
18Can displacement and velocity have opposite signs for a time interval? Yes, in case of an accelerated motion.No, since the sign of the displacement determines the sign of the velocity.There is no relationship between the two quantities.
19Can velocity and acceleration have opposite signs for a time interval? Yes, if the speed is decreasing.Yes, if the object moves to the left.No, since the sign of the velocity determines the sign of the acceleration.
20The sign of acceleration? xMotion in positive directionMotion in negative directionIncreasing speedDecreasing speed
21Sign of acceleration? Depends on Speed increases Speed decreases Coordinate system (choice)Direction of motion relative to coordinate system (choice)Speed increasesIf velocity and acceleration have the same directionSpeed decreasesIf velocity and acceleration oppose each other
22A skier is sliding downhill, starting from rest, at a constant acceleration of 0.5 m/s2. What is his speed as a function of time?After 5.0 s, how far did the skier slide, and how fast is he going?