Chapter 2, Problem 6P

To determine

The average velocity of the given particle.

To identify: Whether average speed of the particle can be obtained from the given data or not.

Answer to Problem 6P

The average velocity of the given particle is found to be $0.78\text{ cm/s}$ . The average speed of the particle cannot be determined from the given data.

Explanation of Solution

Given:

The positions of the particles at the given instants of time:

  $\begin{array}{c}{x}_1=3.4\text{ cm}\\ x_2=8.5\text{ cm}\\ t_1=-2.0\text{ s}\\ t_2=4.5\text{ s}\end{array}$

Formula used:

The average velocity of the particle is given by the following expression:

  $\overline{v}=\frac{x_2-x_1}{t_2-t_1}$

Calculation:

Substitute the values, to find the average velocity.

  $\begin{array}{c}\overline{v}=\frac{x_2-x_1}{t_2-t_1}\\ =\frac{\left(8.5\text{ cm}\right)-\left(3.4\text{ cm}\right)}{\left(4.5\text{ s}\right)-\left(-2.0\text{ s}\right)}\\ =0.78\text{ cm/s}\end{array}$

The average speed of the particle is the ratio of the total distance travelled by the particle in the given time interval. The given data merely specifies the positions of the particle at two instants of time. Using the given data, it is not possible to calculate the distance travelled by the particle. Hence its average speed cannot be calculated.

Conclusion:

Thus, the average velocity of the given particle is found to be $0.78\text{ cm/s}$ . The average speed of the particle cannot be determined from the given data.