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

 

Answers (1)

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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