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Chapter 2: Q82P (page 37)

Figure 2-44 gives the acceleration a versus time t for a particle moving along an x axis. The 鈥榓鈥� axis scale is set by $a_{s} = 12.0 m / s^{2}$ . At $t = 鈥� 2.0 s$ , the particle鈥檚 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

01

Given information

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

02

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

$v_{f} = v_{0} + {鈭�}_{- 2}^{6} a d t$

03

Calculations for the velocity of the particle

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

$v_{f} = v_{0} + {鈭�}_{- 2}^{6} a d t$

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

$a = 2 t$

So,

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

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

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Most popular questions from this chapter

(a) If the maximum acceleration that is tolerable for passengers in a subway train is $1.34 m^{2}$ and subway stations are located $806 m$ apart, what is maximum speed a subway train can attain between stations? (b)What is the travel time between stations? (c) If a subway train stops for localid="1660818170335" $20 s$ at each station, what is the maximum average speed of the train, from one start up to the next? (d) Graph x, v and a versus t for the interval from one start-up to the next?

At time t = 0, a rock climber accidentally allows a piton to fall freely from a high point on the rock wall to the valley below him. Then, after a short delay, his climbing partner, who is 10higher on the wall, throws a piton downward. The positions yof the pitons versus tduring the falling are given in Fig. 2-43. With what speed is the second piton thrown?

Figure 2-18 shows four paths along which objects move from a starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines. Rank the paths according to (a) the average velocity of the objects and (b) the average speed of the objects, greatest

first.

An electric vehicle starts from rest and accelerates at a rate of $2.0 m / s^{2}$ in a straight line until it reaches a speed of 20 m/s. The vehicle then slows at a constant rate of $1.0 m / s^{2}$ until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?

To stop a car, first you require a certain reaction time to begin braking; then the car slows at a constant rate. Suppose that the total distance moved by your car during these two phases is $56.7$ mwhen its initial speed is $80.5 km / h$ , and $24.4$ mwhen its initial speed is $48.3 km / h$ . What are (a) your reaction time and (b) the magnitude of the acceleration?

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