Question

John and Caroline go out for a walk one day. This graph represents their distance from home.

Answer 1

Option (C) is correct as they walked in one direction, then they were still, then they walked in the opposite direction.

Further explanation:

Velocity is defined as the rate of change of displacement with respect to time.

Mathematically,

$\boxed{V=\dfrac{{ds}}{{dt}}}$

Here, $\dfrac{{ds}}{{dt}}$ represent the rate of change of position with respect to time which is also called slope of a curve on position vs time curve.

Case 1:

For constant velocity.

$\boxed{V={\text{constant}}}$  

From the above expression, it can be observed that the rate of change of position with respect to time will be constant. Therefore, the slope of position vs tine curve will also be constant.

The slope of a line is constant throughout the given time interval so position vs time curve will be a straight line passing through the origin.

Case 2:

If velocity of a particle is zero.

Mathematically,  

$\boxed{V=0}$

From the above expression, it can be observed that the rate of change of position with respect to time will be zero. Therefore the slope of position vs tine curve will also be zero.

The slope of a line parallel to X axis is zero throughout the given time interval. So, position vs time curve will be a straight line parallel to the X axis.

Case 3:

If velocity of a particle is constant but the direction of velocity is opposite to the direction of velocity in case 1, in that case the rate of change of position with respect to time will be negative. Therefore, slope will also be negative.

Concept:

The starting curve of a position vs time is a straight line passing through origin whose slope is positive.

This part of curve shows that John and Caroline started walking in one direction with initial velocity zero and reaches a point (let) A.

From A to B curve is a straight line parallel to x axis, therefore John and Caroline are still during this time of interval.

From B to C the curve is a straight line but slope of the line is negative, therefore John and Caroline are walking in the direction opposite with constant velocity.

Thus, option (C) is correct as they walked in one direction, then they were still, then they walked in the opposite direction.

Learn more:

1.  A ball falling under the acceleration due to gravity brainly.com/question/10934170

2.  Conservation of energy brainly.com/question/3943029

3. The motion of a body under friction brainly.com/question/4033012

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

John and carline, walk, graph, distance, home, accurately, one direction, still, opposite direction, velocity, constant, rate of change, position, time, slow, fast.

Answer 2

Answer:

C) They walked in one direction, then they were still, then they walked in the opposite direction.  

Explanation:

John and Caroline go out for a walk one day. This graph represents their distance from home.c According to the graph they walked with almost same in both the direction.

First they walked in one direction and travel 30 meter in same direction then they were still for some time. Then they walked in the opposite direction for 30 meter. They walked in both the direction with approximately equal speed.

Thus, Option C is correct.