# Motion in straight Line

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## Motion in straight Line

17.The displacement of a particle moving in straight line depends on time t as
x=at3+bt2+ct+d

which of the follwing is true
a. Intial acceleration depends on b only
b Intial velocity depends on c only
c. Intial displacement is d
d. Ratio of intial velocity /intial acceleration depends on a and c

Solution(17):
. The displacement of a particle moving in straight line depends on time t as
x=at3+bt2+ct+d

Velocity (dx/dt)=3at2+2bt+c
Acceleration (d2x/dt2)=6at+2b

So Intial displacement(t=0) =d
Intial velolcity(t=0) =c
Intial acceleration (t=0) =2b
18.A particle located at x=0 at time t=0 starts moving along the positive x-direction with a velocity v that varies as
v=√x
The displacement of the particles varies with time as
which of the follwing is true
a. t2
b t3
c. t4
d. t1/2

Solution(18):
. Given v=√x
or
dx/dt=√x
dx/√x=dt
Integrating both sides between the limit (0,x) and (0,t)
x=t2/4
Hence (a) is correct
19.A Train is moving along a straight section of the track with a velocity of 180km/h. The braking deceleration is 2m/s2s
At what distance from a train station should the train driver aply the brake so that train stops at the station
a. 800m
b 625m
c. 700m
d. none of these
Solution(19):
. we are given
v0=180km/h=50m/s
a=-2m/s2
Now v2=v02+2as
0=(50)2-2*2*x or x=625m hence (b) is correct 20.from the previous question,how long will it take to bring the train to the halt
a. 25s
b 20s
c. 15s
d. none of these
Solution(20):
. Now v=v0+at
0=50-2t
or t=25 sec
Hence (a) is correct