Question

Find magnitude of acceleration of particle at \(t = 5\,\text{s}\). If velocity–time graph is given as shown in figure. 

• A. \( \dfrac{u_0}{20} \)
• B. \( \dfrac{u_0}{40} \)
• C. \( \dfrac{u_0}{10} \)
• D. \( u_0 \)

Hint:

Slope of \(v-t\) graph gives acceleration: \[ a = \frac{\Delta v}{\Delta t} \] Straight line in \(v-t\) graph means constant acceleration.

Answer 1

The Correct Option is A

Concept: Acceleration is the slope of the velocity–time graph. \[ a = \frac{dv}{dt} \] Thus the instantaneous acceleration at any time equals the slope of the graph at that point.
Step 1: Determine slope of the first segment of the graph. From the graph, \[ v = 0 \quad \text{at} \quad t=0 \] \[ v = u_0 \quad \text{at} \quad t=20 \]
Step 2: Calculate the slope. \[ a = \frac{u_0 - 0}{20 - 0} \] \[ a = \frac{u_0}{20} \] Since \(t = 5\,\text{s}\) lies in this interval, acceleration remains constant. \[ \boxed{a = \frac{u_0}{20}} \]