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Solved Problem on Kinematics

The motion of a car, which moves with constant speed, is described by the following table

t (h) |
1 | 2 | 4 | 7 | 9 | 11 | 12 |

S (km) |
100 | 200 | 450 | 600 | 400 | 200 | 100 |

from the table data find:

a) The average speed of the car between the instants 1 h and 2 h;

b) The average speed of the car between the instants 4 h and 7 h;

c) The average speed of the car between the instants 9 h and 12 h;

d) The average speed of the car between the instants 1 and 12 h.

Problem diagram

We choose a reference frame oriented to the right.

Solution

a) Using the expression for the average speed

\[ \bbox[#99CCFF,10px]
{v_{\text{m}}=\frac{\Delta S}{\Delta t}=\frac{S_{\text{f}}-S_{\text{i}}}{t_{\text {f}}-t_{\text{i}}}} \tag{I}
\]

\[
v_{\text{m}}=\frac{200-100}{2-1}\\
v_{\text{m}}=\frac{100}{1}
\]

\[ \bbox[#FFCCCC,10px]
{v_{\text{m}}=100\;\text{km/h}}
\]

b) Using the expression (I) for the average speed

\[
v_{\text{m}}=\frac{600-450}{7-4}\\
v_{\text{m}}=\frac{150}{3}
\]

\[ \bbox[#FFCCCC,10px]
{v_{\text{m}}=50\;\text{km/h}}
\]

c) Using the expression (I) for the average speed

\[
v_{\text{m}}=\frac{100-400}{12-9}\\
v_{\text{m}}=-\frac{300}{3}
\]

\[ \bbox[#FFCCCC,10px]
{v_{\text{m}}=-100\;\text{km/h}}
\]

d) Using the expression (I) for the average speed

\[
v_{\text{m}}\;=\;\frac{100-100}{12-1}\\
v_{\text{m}}\;=\;\frac{0}{11}
\]

\[ \bbox[#FFCCCC,10px]
{v_{\text{m}}=0}
\]

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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .