Motion in One Dimension Notes and Example Problems

ü Dt = time in seconds ü Dx= horizontal distance in meters ü Dy = vertical distance in meters ü vi = the initial velocity in m/s ü vf = the final velocity in m/s ü a = acceleration in m/s 2

Acceleration of Gravity • If an object is falling towards the earth surface then you use g or ag = -9. 81 m/s 2. *This means that an object speeds up 9. 8 m/s every second. *It is negative because objects fall downward. • If the object is simply moving, use normal equations to solve for displacement and acceleration.

Ø vav= Dx Dt a = (vf -vi) Dt Dy = vi Dt + ½ a. Dt 2 Ø Ø Ø Dx = ½(vi + vf )Dt vf = vi + a. Dt vf 2 = vi 2 + 2 a. Dx Ø Ø Dy or Dx, depending on what direction the object is accelerating

Problem Solving Tips • • • Anything going down is Object starting from rest Object that is stopping Object at its peak when thrown up When dropping an object, we know • Time up = time down in vertical displacement

Problem Set-Up • Given: Dt = 0. 53 s not stated, but still there vi = 0 m/s a = -9. 8 m/s 2 • Unknown: Dy • Equation: Dy = vi Dt + 1/2 a. Dt 2

Solution vi= 0 m/s so Dy = vi Dt + 1/2 a. Dt 2 since vi = 0 Dy = 1/2 a. Dt 2 Dy = 1/2 (-9. 8 m/s 2)(0. 53 s)2 Dy = -1. 376 m (falling down) • So the table is approximately 1. 4 meters high.

Tom needs to get away from a bomb that Jerry has set. If he uniformly accelerates from rest at a rate of 1. 5 m/s 2, what will his final velocity be when he gets 25 meters away?

Tom and Jerry Problem Set-Up • Given: vi = 0 m/s Dx= 25 m a = 1. 5 m/s 2 • Unknown: vf • Equation: vf 2 = vi 2 + 2 a. Dx

Tom and Jerry Problem Solution vf 2 = vi 2 + 2 a. Dx vf 2 = (0 m/s)2 + 2(1. 5 m/s 2)(25 m) vf 2 = 75 m 2/s 2 vf = 8. 7 m/s Tom will be traveling at 8. 7 m/s.

Problem Set-Up • Given: vi = 16 m/s vf = 0 m/s Dx = 63 m • Unknown: a • Equation: vf 2 = vi 2 + 2 a D x

Solution vf 2 = vi 2 + 2 a D x (0 m/s)2 = (16 m/s)2 + 2 a (63 m) - 256 m 2/s 2 = 2 a (63 m) 2 a = - 256 m 2/s 2 63 m 2 a = -4. 06 m/s 2 a = -2. 03 m/s 2 a = -2. 0 m/s 2

Road Runner Problem Set-Up • Given: vi = 0 m/s a= -9. 8 m/s 2 Dt = 3. 5 s • Unknown: vf and Dy • Equation: a = (vf - vi)/ Dt

Road Runner Problem Solution PART a) a = (vf -vi)/Dt but vi = 0 m/s so (-9. 8 m/s 2) = (vf - 0 m/s)/ 3. 5 s (-9. 8 m/s 2) = vf / 3. 5 s = -34. 3 m/s The piano will hit the ground at a speed of -34 m/s, neglecting the affects of air resistance of course.

Road Runner Problem Solution PART b) • Unknown: Dy • Equation: Dy = vi Dt + 1/2 a. Dt 2

Road Runner Problem Solution PART b) Dy = vi Dt + 1/2 a. Dt 2 but vi = 0 m/s so Dy = 1/2 a Dt 2 = 1/2 (-9. 8 m/s 2)(3. 5 s) 2 = -60. 025 m The piano fell 60. meters.