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 (starts from rest)
a = +10 m/s2
t = 4 seconds
d = ?
• Step 3 - Substitute and Solve Equation:
Δd = Vit + 1/2aΔt2
= 0 m/s(4 sec)+1/2(10 m/s2)(4s)2
Δd = 0 + 5(16)
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 = (6 m/s)2 + 2(2 m/s2)(7 m)
Vf2 = 36 + 4(7)
Vf2 = 64
Vf = 8 m/s