Midterm Survey The survey will be open from now until 11PM Oct 27th (this Sunday) It is at: V4mz5N_2b5p8bdBQzuA_3d_3d (don’t copy that down… it’s posted on the course website)

More on kinematics

Motion at constant acceleration (1D) time 0 t position x 0 x velocity v 0 v acceleration a = constant Average velocity: v av = (x- x 0 )/t and v av = (v + v 0 )/2 x = x 0 + v av t

From the definition of acceleration a = (v - v 0 )/t at = v - v 0 v = v 0 + at

x = x 0 + v av t = x 0 + (v + v 0 ) t /2 = x 0 + (v 0 + at + v 0 ) t /2 x = x 0 + v 0 t + at 2 /2

Motion at constant acceleration v av = (v + v 0 )/2 v = v 0 + at x = x 0 + v 0 t + at 2 /2 v 2 = v a (x- x 0 ) Last equation can be obtained by using the First three ones.

Q1 The magnitude of final velocity increases if 1) the acceleration is along the direction of displacement; 2) the acceleration is opposite to the direction of displacement; 3) the acceleration is along the direction of final velocity; 4) the acceleration is opposite to the direction of final velocity.

Example: Acceleration of the crashing plane An airplane flying at 500km/h crashes into one side of a mountain and stops within 20 m. What is the the acceleration of the plane (if we assume that it is constant)? Displacement = 20 m V 0 =500km/h V f =0 a = ? V 0 =500 km/h

Acceleration of the crashing plane An airplane flying at 500km/h crashes into the side of the mountain and stops within 20 m. What is the the acceleration of the plane (if we assume that it is constant)? Are the units consistent? v 0 =500km/h=500*1000m/3600s  139m/s What is given? x-x 0 = 20m v f = 0 What do we look for? a = ?

Example: Acceleration of the crashing plane An airplane flying at 500km/h crashes into the side of the mountain and stops within 20 m. What is the the acceleration of the plane (if we assume that it is constant)? v 0 =500km/h=500*1000m/3600s  139m/s x-x 0 = 20m v 2 = v a(x-x 0 ) 0= a*20 [m 2 /s 2 = m 2 /s 2 + ( m/s 2 ) * m] a= /40=-483 m/s 2 [m 2 /s 2 /m= m/s 2 ]

Rough estimate: At about 140m/s plane covers 20 meters in 2/7 s. At the same time velocity changes from 100m/s to 0. Acceleration must be negative and approximately 140[m/s]/(2/7)[s] is equal to 490[m/s 2 ]

Q1. Which motion diagram describes the movement of the plane

Q2 If the speed of the incoming plane is 1000km/hr instead of 500km/hr, the distance it moves before stopping will be (assume that the acceleration is the same) 1) 40m; 2) 80m; 3) 20m; 4) None of above.

Q3 If the speed of the incoming plane is doubled, and the acceleration is unchanged, the time it takes for the plane to stop should be 1)halved because the average speed is doubled; 2)four times longer because distance is four times longer; 3) unchanged; 4) doubled.