Suppose that 20 Joules of work is needed to stretch a spring from its natural length of 1 m to 2 m. (a) Determine how much work is needed to stretch the spring from 1.5 m to 2.5 m.
(b) How far beyond its natural length will a force of 500 N keep the spring stretched?

Use the substitution u = √ x to express the integral below in terms of u. Do not evaluate the integral.

Integral sign(√ x /1 + √ x) dx

x + 4/7

step-by-step explanation:

use cymath

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

not sure but it may be b, as i said i'm not sure.