Chapter 2: Q. .31 (page 60)

FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v0x = 8.0 m/s at t0 = 0 s. What is the particle’s velocity at t = 4.0 s?

Short Answer

Expert verified

The velocity of a particle at $t = 4 s$ is 16 m s^-1.

Step by step solution

Given information

Initial velocity of a particle, $v_{0} = 8.0 \frac{m}{s}$

Initial time, $t_{0} = 0 s$

The velocity of a particle.

The change in velocity of a particle $∆ v = v_{f} - v_{0}$ between $t_{0}$ and $t_{f}$ is the area under the curve from $t_{0} = 0 s$ to $t_{f} = 4 s$ . In this case, the curve is a triangle.

Thus, the area of a triangle is

$∆ v =$ area of the triangle between $t_{0} = 0 s$ and $t_{f} = 4 s$ .

$∆ v = \frac{1}{2} \times 4 s \times 4 \frac{m}{s^{2}} = 8 \frac{m}{s}$

Now,

The velocity of a particle at $t_{f} = 4 s$ is given by

$v_{f} = v_{0} +$ area under the acceleration curve $a_{x}$ between $t_{0}$ and $t_{f}$

localid="1648468773258" role="math" $v_{f} = 8.0 \frac{m}{s} + 8 \frac{m}{s} = 16 m / s$

Therefore, the velocity of a particle at $t = 4 s$ is 16 m s^-1. .

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FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v0x = 8.0 m/s at t0 = 0 s. What is the particle’s velocity at t = 4.0 s?

Short Answer

Step by step solution

Given information

The velocity of a particle.

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