# Starting from rest , the acceleration of a particle is a=2(t-1). The velocity of the particle at t=5s is: Option 1) 15 m/sec Option 2) 25 m/sec Option 3) 5m/sec Option 4) None of these

As we discussed in

Velocity -

Rate of change of displacement with time.

Formula $V=\frac{displacement}{time}$

- wherein

E.g. A car moving along a straight line. It moves from O to P (60 m)  in 18 sec and returns from P to O (60 m) in 60 sec
Find velocity.

Acceleration -

Rate of change of velocity with time.

For: a=change in velocity / change in time

$a=\frac{v}{t}$

$a=\frac{v_{f}-v_{i}}{t}$

- wherein

Eg. A car starting from rest accelerates uniformly to a speed of 75 m/s in 12 seconds. What is car’s acceleration ?

$v_{i}=$ 0

$v_{f}=$ 75 m/s

$a=$ ? $a=\frac{v_{f}-v_{i}}{t}$

$=\frac{75-0}{12}$

a = 6.25 m/s2

a= 2(t-1)

$\frac{dv}{dt}=2t-2$

$dv=(2t-2)dt$

$=>\int dv=2\int tdt-2\int dt$

$v=\frac{2t^{2}}{2}-2t$

$=>t^{2}-2t$

given t = 5sec

$v=25-2\times 5$

$=25-10$

15 m/sec

Option 1)

15 m/sec

Option is Correct

Option 2)

25 m/sec

Option is incorrect

Option 3)

5m/sec

Option is incorrect

Option 4)

None of these

Option is incorrect

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