Question

b4-rt10: velocity-time graph ii—work done on box
shown below is a graph of velocity versus time for an object that moves along a straight, horizontal line under the perhaps intermittent action of a single force exerted by an external agent.
rank the work done on the box by the external agent for the 5 - second intervals shown on the graph.
1 greatest
2
3
4 least
or
all the same
all zero
cannot determine
explain your reasoning.

Explanation:

Step1: Recall Work-Energy Theorem

Work done $W = \Delta KE = \frac{1}{2}m(v_f^2 - v_i^2)$, where $m$ = mass, $v_i$ = initial velocity, $v_f$ = final velocity.

Step2: Analyze Interval A (0-5s)

$v_i=0$, $v_f=0$.
$W_A = \frac{1}{2}m(0^2 - 0^2) = 0$

Step3: Analyze Interval B (5-10s)

$v_i=0$, $v_f=-4\ \text{m/s}$.
$W_B = \frac{1}{2}m((-4)^2 - 0^2) = \frac{1}{2}m(16) = 8m$

Step4: Analyze Interval C (10-15s)

$v_i=-4\ \text{m/s}$, $v_f=-4\ \text{m/s}$.
$W_C = \frac{1}{2}m((-4)^2 - (-4)^2) = 0$

Step5: Analyze Interval D (15-20s)

$v_i=-4\ \text{m/s}$, $v_f=4\ \text{m/s}$.
$W_D = \frac{1}{2}m(4^2 - (-4)^2) = \frac{1}{2}m(16-16) = 0$

Answer:

1. B, 2. A, 3. C, 4. D

(Greatest work is done in interval B, while intervals A, C, and D have zero work done)