SOLUTION: A particle moves in a straight line so that its distance, s m, from a fixed point A on the line is given by s=2t^2-4t+9, for t less than or equal to 3, where t is the time in secon

Question 1081862: A particle moves in a straight line so that its distance, s m, from a fixed point A on the line is given by s=2t^2-4t+9, for t less than or equal to 3, where t is the time in seconds after passing through a point B on the line.
(a) the total distance travelled by the particle in the period of t=0 to t=3. Ans=10m
(b) At t=3, the acceleration of the particle is changed to (t − 8)m/s2 , the instantaneous velocity remaining unchanged. Find the next value of t at which the particle comes to instantaneous rest. Ans= 5s
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
a)
.
.
.

.
.
.
.
Looking at the graph, the particle travels from 9 to 7 in the 1st second, from 7 to 9 in the 2nd second and from 9 to 15 in the 3rd second.
So it traveled,

.
.
.
b) Find the instantaneous velocity when ,

So then integrate the new acceleration to get the new velocity,

When ,,

.
.
.
for
.
.
.
Graphing this and looking for the next crossing of the x-axis,
.
.
.

.
.
.
.

.
.
.
You could also factor,

and

RELATED QUESTIONS
A particle moves in a straight line so that its distance, s m, from a fixed point A on... (answered by Alan3354)

A particle moving in a straight line has initial velocity of 2 m/s at a point O on the... (answered by Shin123,ikleyn)

A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where... (answered by ikleyn)

A particle moves in a straight line so that its velocity v m/s is given by v=9-t^2,where (answered by ikleyn)

A particle moves in a straight line so that t seconds its distance from the starting... (answered by Alan3354)

A particle moves in straight line so that t seconds its distance from the starting point... (answered by Alan3354)

A point moves in a straight line so that its distance s from the origin at time t is... (answered by Alan3354)

A particle starts from rest and travels in a straight line so that t seconds after... (answered by rothauserc,ikleyn)

An object is moving in a straight line. The distance (in meters) from a fixed point is... (answered by ikleyn)