Question

A pedestrian left his house and started walking on a straight street, resting at times as necessary. The graph below shows the distance he covered as a function of time. Find the formula describing how his speed depends on the time, and graph this function.

Answer 1

From t= 0 to t=2, distance is a straight line, and hence speed is slope of that line.

Hence for 0<=t<2, speed =
`(8-0)/(2-0) = 4 km/h`

From 2<=t<=2.5, distance remained constant at 8km, hence speed is 0 km/h.

From 2.5<=t<3, distance again a straight lines.

And hence speed = slope of line joining (2.5,8) and (3,10)

=
`(10-8)/(3-2.5)  = (2)/(0.5)  = 4 km/h`

From 3<=t<4, distance remained constant at 10km. That means he is at rest.

Hence speed = 0 km/h for 3<=t<=4.

From 4<=t<5, distance again is a straight line.

Hence speed = slope of line joining (4,10) and (5,12)

=
`(12-10)/(5-4)  = 2 km/h`

Please refer the graph for speed.