1. What is the shortest possible time in which a bacterium could drift at a velocity of 3.5 mm/s across a petri dish with a diameter of 8.4 cm ?

2. A child is pushing a shopping cart at a speed of 1.5 m/s. How long will it take this child to push the cart down an aisle with a length of 9.3 m ?

3. It takes you 9.5 minutes to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance.

What is your displacement ?

Changing Motion

Acceleration

• Acceleration is any change in the velocity of an object with respect to time.

• The difference between two velocities divided by the time for the change.

• Acceleration has a magnitude and direction.

Acceleration

• It measures the rate of change in velocity.

• The SI unit for acceleration is m/s2

(vf –vi )• a = ---------- t

a = acceleration

vf = velocity final

vi = velocity initial t = time

 Example #1

A car increases its velocity from 4 m/s to 25 m/s in 5.5 seconds. Find the car’s acceleration?

G: vi = 4 m/s vf = 25 m/s t = 5.5 s

U: a

(vf –vi )

E: a = ---------- t

S: substitute

S: 3.8 m/s2

Displacement with Constant Uniform Acceleration

• We know that the average velocity is equal to displacement divided by the time interval.

d

v avg = t

• For an object moving with constant acceleration, the average velocity is equal to the average of the initial velocity and the final velocity.

vf + vi

• v avg = 2

Displacement with Constant Uniform Acceleration

d (vf + vi)

t = v avg and v avg = 2

d (vf + vi)

t = v avg = 2

d (vf + vi)t = 2

d = ½ ( vf + vi ) t

Example #2

A car increases its velocity from 4 m/s to 25 m/s in

5.5 seconds. Find the car’s displacement while speeding up.

G: vi = 4 m/s vf = 25 m/s t = 5.5 s

U: d

E: d = ½ ( vf + vi ) t

S: substitute

S: 79.8 m

 Example #3

G: vi = 25 m/s vf = 0 m/s d = 50 m

U: a ( vf – vi )E: a = t d = ½ ( vi + vf ) t

S: substitute

S: -6.3 m/s2

The car’s driver then applies the brakes and stops the car in 50 meters.

Find the car’s acceleration

A car increases its velocity from 4 m/s to 25 m/s in 5.5 seconds.

 Example #4

A car increases its velocity from 4 m/s to 25 m/s in 5.5 seconds. The car’s driver then applies the brakes and stops the car in 50 meters.

Find the time to stop the car.

G:

U:

E:

S:

S: See work on example 3

A golf ball is dropped from a 10-meter tall building, strikes the ground at 12.5 m/s and rebounds at 5 m/s. Find the ball’s acceleration from the point it is dropped until it strikes the ground, if the time of impact equaled 0.025 seconds.

G: d = 10 m vi = 0 m/s vfdown = 12.5 m/s (down) vfup = 5 m/s (up) t = 0.025 s

U: a ( vf – vi )E: a = t

S: substitute

S: 500 m/s2

Example #5