Chapter 2: Q82P (page 37)

Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The ‘a’ axis scale is set by $a_{s} = 12.0 m / s^{2}$ . At $t = ‐ 2.0 s$ , the particle’s velocity is 7.0 m/s. What is its velocity at $t = 6.0 s$ ?

Short Answer

Expert verified

The velocity of the particle at $t = 6.0 s$ isrole="math" localid="1660885428340" $39 m / s$

Step by step solution

Given information

$a_{s} = 12.0 m / s^{2} t = - 2.0 s v_{0} = 7.0 m / s$

Kinematic Equations of Motion

Kinematics is the study of how a system of bodies moves without taking into accounts the forces or potential fields that influence the motion. The equations which are used in the study are known as kinematic equations of motion.

Formula:

The final velocity is given by

$v_{f} = v_{0} + \int_{- 2}^{6} a d t$

Calculations for the velocity of the particle

The velocity of the particle at $t = 6.0 s e c$ can be calculated as,

$v_{f} = v_{0} + \int_{- 2}^{6} a d t$

From thegiven graph the acceleration as a function of t can be written as,

$a = 2 t$

So,

$v_{f} = v_{0} + \int_{- 2}^{6} 2 t d t v_{f} = 7 + 2 {[\frac{t^{2}}{2}]}_{- 2}^{6} v_{f} = 7 + 32 = 39 m / s$

Hence, the velocity of the particle will be 39 m/s

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Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The ‘a’ axis scale is set by $a_{s} = 12.0 m / s^{2}$ . At $t = ‐ 2.0 s$ , the particle’s velocity is 7.0 m/s. What is its velocity at $t = 6.0 s$ ?

Short Answer

Step by step solution

Given information

Kinematic Equations of Motion

Calculations for the velocity of the particle

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Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The ‘a’ axis scale is set by as=12.0m/s2. Att=‐2.0s, the particle’s velocity is 7.0 m/s. What is its velocity att=6.0s?

Short Answer

Step by step solution

Given information

Kinematic Equations of Motion

Calculations for the velocity of the particle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Translational Dynamics

Kinematics Physics

Wave Optics

Modern Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The ‘a’ axis scale is set by $a_{s} = 12.0 m / s^{2}$ . At $t = ‐ 2.0 s$ , the particle’s velocity is 7.0 m/s. What is its velocity at $t = 6.0 s$ ?