4.2. Solved Examples: Linear Motion
Solved Examples
Example 1
A car starts from rest and accelerates at a rate of [latex]2.1\mathrm{m/s^2}[/latex] for [latex]10\, \text{s}[/latex]. Find the final velocity of the car.
Given:
[latex]v_i[/latex] = [latex]0\mathrm{m/s}[/latex]
[latex]a[/latex] = [latex]2.1\mathrm{m/s^2}[/latex]
[latex]t[/latex] = [latex]20\, \text{s}[/latex]
[latex]v_i[/latex] = [latex]0\mathrm{m/s}[/latex]
[latex]a[/latex] = [latex]2.1\mathrm{m/s^2}[/latex]
[latex]t[/latex] = [latex]20\, \text{s}[/latex]
Find:
[latex]v_f[/latex] = [latex]?[/latex]
[latex]v_f[/latex] = [latex]?[/latex]
Solution:
-
- Decide which equation works for the question by examining what information is given and what needs to be found.
[latex]a = \frac{v_f - v_i}{t}[/latex]
- Rearrange the equation to express the wanted quantity:
[latex]v_f = v_i + at[/latex]
- Substitute the values for the known quantities in the last equation:
[latex]v_f = 0 + 2.1 \times 10 = 21 \, \text{m/s}[/latex]
- Decide which equation works for the question by examining what information is given and what needs to be found.
Answer:
[latex]v_f = 21 \text{m/s}[/latex]
Example 2
A truck travelling at 25 m/s slows down to 10 m/s in 100 m. Find the truck’s acceleration.
Given:
[latex]v_i[/latex] = [latex]25\mathrm{m/s}[/latex]
[latex]v_f[/latex] = [latex]10\mathrm{m/s}[/latex]
[latex]s[/latex] = [latex]100m[/latex]
[latex]v_i[/latex] = [latex]25\mathrm{m/s}[/latex]
[latex]v_f[/latex] = [latex]10\mathrm{m/s}[/latex]
[latex]s[/latex] = [latex]100m[/latex]
Find:
[latex]a[/latex] = [latex]?[/latex]
[latex]a[/latex] = [latex]?[/latex]
Solution:
-
- Decide which equation works for the question by examining what information is given and what needs to be found.
[latex]v_f^2 = v_i^2 + 2aS[/latex]
- Rearrange the equation to express the wanted quantity:
[latex]a = \frac{v_f^2 - v_i^2}{2S}[/latex]
- Substitute the values for the known quantities in the last equation:
[latex]a = \frac{10^2 - 25^2}{2 \times 100} = -2.6 \, \text{m/s}^2[/latex]
- Decide which equation works for the question by examining what information is given and what needs to be found.
Answer:
[latex]a = -2.6 \, \text{m/s}^2[/latex]
