A three-wheeler starts from rest, accelerates uniformly with 1 m s–2 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1,2,3….) versus n. What do you expect this plot to be during accelerated motion : a straight line or a parabola ?
Given: The acceleration of three wheeler is 1 ms − 2 and time is 10 s .
Since the three-wheeler starts from rest, therefore the initial speed of three-wheeler is 0 m / s .
The distance travelled by three-wheeler in n t h is given as,
s n = u t n + a ( 2 n − 1 ) 2
Where, s n is the distance travelled in the n th second, u is the initial speed of the three-wheeler, t n is the time taken, a is the acceleration of the three-wheeler and n is a constant.
By substituting the values in the above expression, we get
s n = ( 0 × t n ) + ( 1 × ( 2 n − 1 ) 2 ) = 0.5 ( 2 n − 1 )
The distance covered in suitable time intervals is shown in the table below.
t n 1 2 3 4 5 6 7 8 9 10 D n = 0.5 ( 2 n − 1 ) 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
The plot between distances covered by the three-wheeler during n t h second versus n is as follows.
Hence, the plot during accelerated motion is a straight line.
Given: The acceleration of three wheeler is
Since the three-wheeler starts from rest, therefore the initial speed of three-wheeler is
The distance travelled by three-wheeler in
Where,
By substituting the values in the above expression, we get
The distance covered in suitable time intervals is shown in the table below.
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| | 0.5 | 1.5 | 2.5 | 3.5 | 4.5 | 5.5 | 6.5 | 7.5 | 8.5 | 9.5 |
The plot between distances covered by the three-wheeler during
Hence, the plot during accelerated motion is a straight line.
