B. 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 (Object starts from rest)

a = +10 m/s2

t = 4 seconds

d = ?

 

• Step 3 - Substitute and Solve Equation:

 Δd = Vit + 1/2aΔt2

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

 

Answer: Δd = 80 m

 

C. 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 7m 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 7m 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  =(6m/s)2 + 2(2 m/s2)(7 m)

 

Answer: Vf = 8 m/s