Question

A person travelling on a straight line moves with a uniform velocity \( v_1 \) for a distance \( x \) and with a uniform velocity \( v_2 \) for the next \( \frac{3x}{2} \) distance. The average velocity in this motion is \( \frac{50}{7} \, \text{m/s} \). If \( v_1 \) is 5 m/s, then \( v_2 \) is ___ m/s.

Hint:

When calculating average velocity in non-uniform motion, break the total distance and time into separate parts. Apply the formula \( v_{\text{avg}} = \frac{total distance}{total time} \) to each segment and solve for the unknown variable.

Answer 1

Correct Answer: 10

Given: \[ v_{\text{avg}} = \frac{x_1 + x_2}{t_1 + t_2} \] Where \( x_1 = x \), \( x_2 = \frac{3x}{2} \), \( v_1 = 5 \, \text{m/s} \), and \( v_2 \) is the unknown velocity. Substituting the values: \[ v_{\text{avg}} = \frac{50}{7} \, \text{m/s} \] \[ \Rightarrow \frac{50}{7} = \frac{x + \frac{3x}{2}}{\frac{x}{v_1} + \frac{3x}{2v_2}} \] \[ \Rightarrow \frac{50}{7} = \frac{\frac{5x}{2}}{\frac{x}{5} + \frac{3x}{2v_2}} \] Simplifying the equation: \[ \Rightarrow \frac{50}{7} = \frac{5x}{2} \times \frac{5}{x} \quad \text{(by cross-multiplying)} \] \[ \Rightarrow v_2 = 10 \, \text{m/s} \]