Acceleration and Instantaneous Velocity Distance vs Displacement You

Acceleration and Instantaneous Velocity

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 displacement (with equations using the same symbols!)

Average Speed • Two ways to look at it

Acceleration • Acceleration is a VECTOR quantity • Units: Units of v is m/sec; units of t is sec • Units of a is m/sec 2

What is the velocity at each point? What is the average velocity? Distance vs. Time 12 Distance 10 8 6 V 4 2 0 0 5 10 15 20 Time 25 30 35

What is velocity? What is Instantaneous velocity? is made very small – infinitesimally small

What is happening to the velocity in this diagram?

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 V 3 V 2 V 1

Acceleration is a change in velocity over time. V 3 V 2 V 1

Is there a meaning to the area under the line? Velocity versus Time 12 Velocity 10 8 6 V 4 2 0 0 5 10 15 20 Time 25 30 35

d=vt The area under the curve is given by v * t. The area under the curve is the distance. Velocity versus Time 12 Velocity 10 8 6 V 4 2 0 0 5 10 15 20 Time 25 30 35

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 • (d = 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 10 m/sec (22 miles/hour) and accelerates at a rate of 1 m/sec (1 m/sec 2) 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. 8 m/sec 2 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 Equation. S and Units