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 start, then becoming slower Constant speed Which car has the highest average speed? Draw the x-t graph for the three cars. Draw the v-t graph for the three cars.

Reading assignment 2.2 Which 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

Reading 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? vx t x t B. A. vx t vx t C. D.

Reading Assignment: A. B. C. D. Which of the following is a correct equation for the instantaneous acceleration in x direction? A. B. C. D.

Instantaneous velocity Constant speed: straight line in x-t graph Slope = velocity = average velocity What happens if the velocity is not constant?

Instantaneous velocity The sled becomes faster as it goes downhill. Which of the following curves does best represent position versus time for the sled? B x C D A t

Instantaneous velocity The sled becomes faster as it goes downhill. Which of the following curves does best represent position versus time for the sled? x C t

Instantaneous velocity x(t) position x is a function of time t x x2 x1 t t1 t2 velocity at time t1 ?

Instantaneous velocity x x3 x1 t t1 t3 t2 velocity at time t1 ?

Instantaneous velocity x x4 x1 t t1 t4 t3 t2 velocity at time t1 ?

Instantaneous velocity x t t1 velocity at time t1 ?

Instantaneous velocity velocity at time t1 ?

Instantaneous velocity is the first derivative of distance with respect to time Slope in x-t graph Unit of measurement: 1 m/s Speed is the magnitude of the instantaneous velocity

Instantaneous velocity - example A robot is logging its position as a function of time, given below. Sketch the graph of velocity versus t. Position x Time t t1 t2

A 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 equation Find 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.

Sketch 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. v t Sketch a-t and x-t graphs.

Example: 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.

Can 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.

Can 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.

The sign of acceleration? x Motion in positive direction Motion in negative direction Increasing speed Decreasing speed

Sign of acceleration? Depends on Speed increases Speed decreases Coordinate system (choice) Direction of motion relative to coordinate system (choice) Speed increases If velocity and acceleration have the same direction Speed decreases If velocity and acceleration oppose each other

A 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?