4.2. Solved Examples: Linear Motion
Example 1
A car starts from rest and accelerates at a rate of [latex]2.1 \text{ } \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 \text{ } \text{ m/s}[/latex]
[latex]a[/latex] = [latex]2.1 \text{ } \text{ m/s}^2[/latex]
[latex]t[/latex] = [latex]20 \text{ s}[/latex]
[latex]v_i[/latex] = [latex]0 \text{ } \text{ m/s}[/latex]
[latex]a[/latex] = [latex]2.1 \text{ } \text{ 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]
Answer:
[latex]v_f = 21 \text{ m/s}[/latex]
Example 2
A truck travelling at [latex]25 \text{ m/s}[/latex] slows down to [latex]10 \text{ m/s}[/latex] in [latex]100 \text{ m}[/latex]. Find the truck’s acceleration.
Given:
[latex]v_i[/latex] = [latex]25 \text{ m/s}[/latex]
[latex]v_f[/latex] = [latex]10\text{ m/s}[/latex]
[latex]s[/latex] = [latex]100 \text{ m}[/latex]
[latex]v_i[/latex] = [latex]25 \text{ m/s}[/latex]
[latex]v_f[/latex] = [latex]10\text{ m/s}[/latex]
[latex]s[/latex] = [latex]100 \text{ m}[/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]
Answer:
[latex]a = -2.6 \, \text{m/s}^2[/latex]
