Question

velocity vs time
the velocity of a 1.3 kg remote - controlled car is plotted on the graph.
the work of segment a is
j.
options: 585, 735, 1170, 2345

Explanation:

Step1: Determine final velocity in segment A

From the velocity - time graph, at the end of segment A (t = 1s), the velocity \(v = 30\space m/s\) (assuming the y - axis scale, since at t = 1, the velocity reaches 30 m/s as per the graph's first segment). The initial velocity \(u = 0\space m/s\) (starts from rest). The mass of the car \(m=1.3\space kg\).

Step2: Use work - energy theorem

The work - energy theorem states that the work done \(W\) on an object is equal to the change in its kinetic energy \(\Delta KE\). The formula for kinetic energy is \(KE=\frac{1}{2}mv^{2}\). The change in kinetic energy \(\Delta KE=\frac{1}{2}m(v^{2}-u^{2})\). Since \(u = 0\), \(\Delta KE=\frac{1}{2}mv^{2}\).

Substitute \(m = 1.3\space kg\) and \(v=30\space m/s\) into the formula:

\(W=\Delta KE=\frac{1}{2}\times1.3\times(30)^{2}\)

First, calculate \((30)^{2}=900\). Then, \(\frac{1}{2}\times1.3\times900 = 0.65\times900=585\space J\)

Answer:

585