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A three wheeler starts from rest, accelr...

A three wheeler starts from rest, accelrates uniformly with ` 1 ms^(-2)` on a straight road for ` 10 s` and then moves with uniform velocity . Plot a graph between the distance coverd by the vehicle during the nth second ( n = 1,2,3, ……..) v ersus (n) What do you expect the plot to be during acclerated motion: a straight line or a parabola ?
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Text Solution

Verified by Experts

Here, ` u= 0 , a=1 ms^(-2)`
Distance covered in nth second is
` D_n =u q/2 ( 2n - 1) =0 + 1/2 ( 2n -1) = 0.5 (2 n -1)` …(i)
Putting ` n= 1,2,3, …….., we can find the value of ` D_n`. The various values of (n) and corresponding values of ` D_n` are shown below :
`|{:(n,1,2,3,4,5,6,7,8,9,10),(D_(n),0.5,1.5,2.5,3.5,4.5,5.5,6.5,7.5,8.5,9.5):}|`
On plotting a graph between ` D_n` and ` n`,we gert a st. `AB` as show in Fig. 2 . (CNT). 11. From (1) , ` D_n prop n` so the graph is a straph si a straight line. After ` 10 s` the graph is a straight line ` BC` parallel to time axis.
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Knowledge Check

  • A car starts from rest and accelerates at a constant rate in a straight line. In the first second, the car covers a distance of 2.0 meters. How much additional distance will the car cover during the second second of its motion ?

    A
    2.0 m
    B
    6.0 m
    C
    4.0 m
    D
    8.0 m

  • A particle moving in a straight line covers half the distance with speed v_(0) . The other half of the distance is covered in two equal time intervals with speed v_(1) and v_(2) , respectively. The average speed of the particle during this motion is

    A
    `(v_(0)(v_(1)+v_(2)))/(v_(0)+v_(1)+v_(2))`
    B
    `(2v_(0)(v_(1)+v_(2)))/(v_(0)+v_(1)+v_(2))`
    C
    `(2v_(0)(v_(1)+v_(2)))/(2v_(0)+v_(1)+v_(2))`
    D
    `(v_(0)(v_(1)+v_(2)))/(2v_(0)+v_(1)+v_(2))`