Question

Question 3.23 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?

Chapter Motion In A Straight Line Page 59

Answer 1

Given ,
Initial velocity = 0 m/s
Acceleration = 1 m/s^2
We know,
Distance covered in nth second = u + (2n-1) a/2
e.g. Snth = 0 +(2n-1)/2
Snth = (2n-1)/2 = n - 1/2
Here we see Snth directly proportional ton e.g Snth linearly varies witn n . Hence, graph must be straight line not a parabola.

Answer 2

Straight Line

To Find the distance covered by the body we have the following relation:

Dn = u + $\frac{a}{2}$(2n - 1)--------(i)

Here,

D is the distance covered by the body.

U is the initial velocity of the body.

a is the acceleration of the body.

n = Time, 1,2,3 ...n

In this case:

a = 1 m/sec^2 and u = 0

Dn = 1/2 (2n - 1) -------(ii)

This relation tells us that:

Dn ∝ n ------(iii)

Now when we substitute different value of n in equation 3 we get,

n    1      2    3   4      5   6     7    8     9   10

Dn 0.5  1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

When we plot these points on a graph paper we get a straight line. The graph is attached below.

This three wheeler attains the uniform velocity after 10 seconds so the line which is drawn would be parallel to the time axis n here = 10 secs.