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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 mtox=3 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 m.

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 – Initial Position

=5 m−9 m=−4 m


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

A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of\({\bf{6}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{5}}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\)for\({\bf{8}}{\bf{.10 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}\;{\bf{s}}\). What is its muzzle velocity (that is, its final velocity)?

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is\({\bf{2}}{\bf{.10 \times 1}}{{\bf{0}}^{\bf{4}}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\), and 1.85 ms (\({\bf{1}}\;{\bf{ms = 1}}{{\bf{0}}^{{\bf{ - 3}}}}\;{\bf{s}}\)) elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

Figure 2.68 shows the displacement graph for a particle for 5 s. Draw the corresponding velocity and acceleration graph

Construct the displacement graph for the subway shuttle train as shown in Figure 2.18(a). Your graph should show the position of the train, in kilometres, from t = 0 to 20 s You will need to use the information on acceleration and velocity given in the examples for this figure.

A coin is dropped from a hot-air balloon that is 300m above the ground and rising at 10.00 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

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