Acceleration

Distance vs. Displacement You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (yellow arrow). What if you drove in a circle? start stop

Speed Speed is distance / time or more accurately

Velocity is speed in a given direction

Constant speed A moving object that doesn’t change it’s speed travels at constant speed Constant speed means equal distances are covered in an equal amount of time What is the equation of the blue line?

What is the velocity at each point? What is the average velocity?

m = m/s * sec What is velocity? m/sec = m/sec

What is average velocity? m/sec = m/sec What is average velocity? for some interval v = (df - di) / (tf – ti)

Average velocity: v = (df - di) / (tf – ti) for some interval v = (df - di) / (tf – ti) What is Instantaneous velocity? is made very small – infinitesimally small

What is happening to the velocity in this diagram?

Instantaneous velocity

Finding instantaneous velocity Find the slope using small values of t and d. Find the tangent to the line of d vs t.

Instantaneous velocity

Acceleration is a change in velocity over time.

Acceleration Acceleration is Acceleration is a VECTOR quantity Units: Units of v is m/sec;units of t is sec Units of a is m/sec2

Is there a meaning to the area under the line?

d = v t The area under the curve is given by v * t. The area under the curve is the distance.

Instantaneous and Average Velocity http://www. youtube. com/watch

Questions What if acceleration is in the same direction as velocity? What if acceleration is in the opposite direction from velocity?

Equations  v = (df - di) / t vt = (df - di )  df = di + vt  (vf – vi)/t = a (vf – vi) = at  vf = vi + at We usually ignore Dt = (tf – ti) and just use t since we can arbitrarily start the clock when we declare t=0

Examples Asher is driving at 10m/sec (22 miles/hour) and accelerates at a rate of 1m/sec/sec (1m/sec2) for a period of 10 seconds. What is Asher’s final velocity? Sarah jumps out of an airplane. Her initial vertical velocity was 0 m/sec. Gravity accelerates a falling body at a rate of 9.8m/sec2 near the surface of the Earth. What is Sarah’s velocity after 5 seconds of free fall? What is this in mph? If Sarah keeps falling for another 5 seconds, will her velocity double? (Hint: Sarah is falling “spread-eagled”)

SAWITESU Show All Work Including The EquationS and Units