Question

Velocity versus time graph is given. Find the magnitude of acceleration of the particle at t = 5 s.

• A. \( \dfrac{u_0}{10} \)
• B. \( \dfrac{u_0}{20} \)
• C. \( \dfrac{u_0}{5} \)
• D. \( \dfrac{u_0}{4} \)

Answer 1

The Correct Option is B

Concept:
Acceleration is the slope of the velocity–time graph. \[ a = \frac{dv}{dt} \] For straight-line segments in a velocity-time graph, acceleration is constant and equal to the slope of the line. Step 1: Identify the interval for \(t = 5\,\text{s\).} From the graph, between \(t=0\) and \(t=20\,\text{s}\), velocity increases linearly from \(0\) to \(u_0\). Thus acceleration in this interval is constant. Step 2: Calculate slope (acceleration). \[ a = \frac{\Delta v}{\Delta t} \] \[ a = \frac{u_0 - 0}{20 - 0} \] \[ a = \frac{u_0}{20} \] Step 3: Acceleration at \(t=5\,\text{s\).} Since acceleration is constant in this region: \[ a = \frac{u_0}{20} \] \[ \boxed{\frac{u_0}{20}} \]