Question

The given figure is a graph of the coordinate of a spider crawling along the $x$ -axis.

(a) Graph its velocity and acceleration as functions of time.

(b) In a motion diagram, show the position, velocity and acceleration of the spider at the five times: $t = 2.5 s, t = 10 s$ , $t = 20 s, t = 30 s$ and $t = 37.5 s$ .

Accepted Answer

(a) $v_{x}$ is the slope of the $x$ versus $t = 2.5 s, t = 10 s$ curve and $a_{r}$ is the slope of the $v_{x}$ versus $t$ curve.

$t = 0$ to $t = 5 s : x$ versus $t$ is a parabola, so $a_{x}$ is a constant. The curvature is positive, so $a_{x}$ is positive. $v_{x}$ versus $t$ is a straight line with positive slope. $v_{0 x} = 0$ .

$t = 5 s$ to $t = 15 s : x$ versus $t$ is a straight line, so $v_{x}$ is constant and
0. $a_{x} = 0 .$ The slope of $x$ versus $t$ is positive, so $v_{x}$ is positive.
$t = 15 s$ to $t = 25 s : x$ versus $t$ is a parabola with negative curvature, so $a_{x}$ is constant and negative. $v_{x}$ versus $t$ is a straight line with negative slope. The velocity is zero at $20 s$ , positive to $15 s$ to $20 s$ and negative to $20 s$ to $25 s$ .

$t = 25 s$ to $t = 35 s : x$ versus $t$ is a straight line, so $v_{x}$ is constant and $a_{x} = 0 .$ The slope of $x$ versus $t$ is negative, so $v_{x}$ is negative.
$t = 35 s$ to $t = 40 s : x$ versus $t$ is a parabola with positive curvature, so $a_{x}$ is constant and positive.

$v_{x}$ versus $t$ is a straight line with positive slope. The velocity reaches
zero at $t = 40 s$ .
The graphs of $v_{x} (t)$ and $a_{x} (t)$ are sketched in the figure.

(b) The motions diagrams are sketched in the figure.

The spider speeds up for the first $5 s$ , since $v_{x}$ and $a_{x}$ are both positive. Starting at $t = 5 s$ , the spider starts to slow down, stops momentarily at $t = 20 s$ and then moves in the opposite direction. At $t = 35 s$ , the spider starts to slow down again and stops at $t = 40 s$ .

B M Sharma Solutions for Chapter: Kinematics I, Exercise 64: ILLUSTRATION 4.60

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Kinematics I, Exercise 64: ILLUSTRATION 4.60

Questions from B M Sharma Solutions for Chapter: Kinematics I, Exercise 64: ILLUSTRATION 4.60 with Hints & Solutions

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