Before You Begin

Question #43483

Difficulty: 8/10 | 🟢 Free

The Question

The velocity-time ( $v-t$ ) graph of a particle moving along the x-axis exhibits changing concavity and is modeled by the equation $v(t) = 4t^3 - 12t^2 + 16$ , where $v$ is in $\text{m/s}$ and $t$ is in seconds. Determine the average speed of the particle over the time interval from $t = 0$ to $t = 3 \text{ s}$ .

Options

A.
$7 \text{ m/s}$
B.
$10 \text{ m/s}$
C.
$16 \text{ m/s}$
D.
$21 \text{ m/s}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Non-Uniform Acceleration Constraint|Graphical Concavity Significance|Average Speed Ambiguity

Why This Question Is Tricky

Common Mistakes

This question tests the fundamental definition of average speed for non-uniformly accelerated motion.

Students often fall into the trap of using the kinematic shortcut $v_{avg} = (u+v)/2$ , which yields $16 \text{ m/s}$ here.

This formula is strictly valid only for constant acceleration (linear $v-t$ graphs).

By providing a cubic $v-t$ function with an inflection point, the acceleration is explicitly non-uniform and changes sign.

The correct approach requires recognizing that average speed is the time-averaged integral of the velocity function, forcing the use of calculus.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Non-Uniform Acceleration Constraint
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free