a = 5 m/s^2
STEP1: Identify knowns & unknowns.
This question is asking to find acceleration with knowns of final velocity, initial velocity, and elapsed time.
STEP 2: Identify the related formula. This is the formula used for problems related to Velocity after constant acceleration over time.
vf=vi+atmodified v sub f with boxed outline space equals modified v sub i with boxed outline space plus modified a with boxed outline space modified t with boxed outline space\(\xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{v_{f}}\, =\xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{v_{i}}\, +\xpmhighlightbox{bgcolor=#244D57, underlinecolor=#D8F8FF, linestyle=dashed}{a}\, \xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{t}\, \)
vf=vi+atmodified v sub f with boxed outline space equals modified v sub i with boxed outline space plus modified a with boxed outline space modified t with boxed outline space\(\xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{v_{f}}\, =\xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{v_{i}}\, +\xpmhighlightbox{bgcolor=#244D57, underlinecolor=#D8F8FF, linestyle=dashed}{a}\, \xpmhighlightbox{bgcolor=#433C65, underlinecolor=#F3E8FD}{t}\, \)
STEP 3: Input variables, solve and simplify
a. Identify knowns
vf=15 m/svi=5 m/st=2 s3 lines; Line 1: v sub f equals 15 space m / s; Line 2: v sub i equals 5 space m / s; Line 3: t equals 2 space s end lines;\(v_{f}=15~\mathrm{m}/\mathrm{s}\\ v_{i}=5~\mathrm{m}/\mathrm{s}\\ t=2~\mathrm{s}\)
b. Plug in values
15 m/s=5 m/s+a⋅2 s15 space m / s equals 5 space m / s plus a center dot 2 space s\(15~\mathrm{m}/\mathrm{s}=5~\mathrm{m}/\mathrm{s}+a\cdot 2~\mathrm{s}\)
c. Re-order terms so constants are on the left
15 m/s = 5 m/s + 2s • a
d. Rearrange terms
15 m/s = 2s • a + 5 m/s
e. Subtract 5 m/s from both sides
15 m/s - 5 m/s = 2s • a + 5 m/s - 5 m/s
f. Simplify
10 m/s = 2s • a
g. Divide both sides by the same factor
10m|s/2s = 2s • a/2s
h. Simplify
a = 5 m/s^2
STEP 4: Check unit of measurement
Acceleration is measured in meters per second squared.
a = 5 m/s^2