FIGURE Q2.7 shows the position-versus-time graph for a moving

object. At which lettered point or points:

a. Is the object moving the fastest?

b. Is the object moving to the left?

c. Is the object speeding up?

d. Is the object turning around?

A graph showing an object at different position at different time is known as distance -time graph. The slope of this graph gives the value of speed . is moving such that at six different points the slope of position-time graph is different.

At point C, the slope of x-t graph is the steepest. So at point C the object is moving the fastest.

A tangent to the position-time curve of the given object determines its velocity.

In the given graph, the slope of the curve at point F is negative. Which means, if we consider the positive x-axis as positive then at F , the object is moving in negative direction or towards the starting point.

So, from point F, the object is moving towards left.

The direction of the slope of velocity curve with positive x-axis determines whether the object is moving to the right of to the left.

From point B, the slope of the curve is heading towards positive value or the magnitude of the slope is increasing. So from point B, the object is speeding up.

At point E the tangent to the x-t curve is parallel to positive x-axis.

The slope of position-time curve is zero at point E. After this point , the slope is becoming negative . The curve is taking a turn round, reversing its direction of motion , from point E.