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Chapter 2: Q4PE (page 82)

Find the following for path D in Figure 2.59:

(a) The distance travelled.

(b) The magnitude of the displacement from start to finish.

(c) The displacement from start to finish.

Short Answer

Expert verified

a) 8 m

b) 4 m

c) -4 m

Step by step solution

01

Distance and displacement

The distance is the whole length of the body's journey. The meter is the unit of measurement. It's a number that represents a scalar value.

The shortest distance between the beginning and finishing points is defined as displacement. It's a quantity that's been given a vector. The length is given in meters.

The distance and displacement will be the same only if the voyage is in a straight line.

02

For particle D distance and displacement

Figure: Path of particle D

a. The distance travelled by the particle D is :


First, it goes fromx=9鈥�mtox=3鈥�m. The total distance covered is 6m. Then the body comes back till 5m, so it covers more distance. Now the total distance will be 6+2=8鈥尘.

Thus, the distance covered by particle D is 8m.

b. The magnitude of the displacement, in this case, will not be the same as the distance as it is not a straight path.


Displacement of the particle D =Final position 鈥� Initial Position

=5鈥尘鈭�9鈥尘=鈭�4鈥尘


Thus, the magnitude will be 4 m.



c. The direction of the displacement would be -4mas the body is moving in the negative x-direction.

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Most popular questions from this chapter

While entering a freeway, a car accelerates from rest at a rate of\({\bf{2}}{\bf{.40}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\)for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer is reasonable. (d) What is the car鈥檚 final velocity? Solve for this unknown in the same manner as in part (c), showing all steps explicitly.

(a) A world record was set for the men鈥檚 100 mdash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt 鈥渃oasted鈥� across the finish line with a time of . If we assume that Bolt accelerated for3.00 sto reach his maximum speed, and maintained that speed for the rest of the race, calculate his maximum speed and his acceleration.

(b) During the same Olympics, Bolt also set the world record in the200 mdash with a time of 19.30 s Using the same assumptions as for the 100 mdash, what was his maximum speed for this race?

Find the following for path A in Figure 2.59:

(a) The distance travelled.

(b) The magnitude of the displacement from start to finish.

(c) The displacement from start to finish.

Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t = 10 s is 0.208 m/s. Assume all values are known to 3 significant figures.

Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
See all solutions

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