An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by
where v is the instantaneous speed. The time taken by the object, to come to rest, would be :
\(\int\limits_{6.25}^0 {\frac{{dv}}{{\sqrt v }} = - 2.5\int\limits_0^t {dt} } \)
\(\left| {2\sqrt \upsilon } \right|_{6.25}^0 = - 2.5t\)
\(2\sqrt {6.25} = 2.5t\)
t = 2 sec.
Given the deceleration equation: , where v is instantaneous speed. We need to find the time taken for the object to come to rest (v=0) from initial speed 6.25 m/s.
Rearrange the equation to separate variables v and t:
Integrate from initial condition (t=0, v=6.25) to final condition (t=T, v=0):
Left side:
Right side:
Equate both sides:
Therefore: seconds
The time taken by the object to come to rest is 2 seconds (Option 2).
General form:
Solution method:
Power rule for integration: