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Ever see an object roll UP hill?

 

 

 

C. Solving Word Problems

 

 

 

 

ex) A car accelerates uniformly from rest at a rate of +10 m/s2. How far will the car travel in 4 seconds?

 

 

• Step 1 - Read and underline all the important information

 

 

ex) A car accelerates uniformly from rest at a rate of +10 m/s2. How far will the car travel in 4 seconds?

 

  

Step 2 - Turn all your information into letters

 

Vi = 0 (starts from rest)

a = +10 m/s2

t = 4 seconds

d = ?

 

 

Step 3 - Substitute and Solve Equation:

 

 

 

 Δd = Vit + (1/2)aΔt2

 

= 0 m/s(4 sec)+1/2(10 m/s2)(4s)2

 

 

Δd = 0 + 5(16)

 

 

Δd = 80 m

 

 

D. Deriving the 2nd displacement equation:

 
Vf2 = Vi2 + 2aΔd
 
 
d = VΔt
 
 
 

Δd

=

(Vf + Vi) Δt
   

2

 
	
 
 
 
 
 
 
 
 since Vf = Vi + aΔt  
then Δt = (Vf -Vi)/a
 
 
 
 
 
 
Δd = (Vf + Vi) (Vf - Vi)

2

a

 

Δd =

(Vf2 - Vi2)

2a

Cross Multiply
 
 
 
 
 
	

2aΔd = Vf2 - Vi2

 
Vf2 =(Vi2 + 2aΔd)

 

 

 

Ex) A car with an initial velocity of +6m/s accelerates at a rate 2 m/s2. Find the cars final velocity after it travels 7 m from its initial position

"Step 1 - Read and

underline all the

 important information "

 

Ex) A car with an initial velocity of +6m/s accelerates at a rate 2 m/s2. Find the cars final velocity after it travels 7 m from its initial position

 

"Step 2 - Turn all

your information

 into letters"

 

 

Vi = 6m/s
a = 2 m/s2
Vf = ?
d = 7 meters

 

"Step 3 - Substitute

and Solve"

 

 

 

 

 

Vf2 = Vi2 + 2ad

 

Vf2  = (6 m/s)2 + 2(2 m/s2)(7 m)

 

 

 

Vf2  = 36 + 4(7)

 

Vf2 = 64

 

 

Vf = 8 m/s

 

 

 

 

Displacement
Plots

 

 

 

 

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