Question

1. At which of the six number points does the particle have no (zero) acceleration?
2. At which of the six number points does the particle have the greatest displacement if it started from x = 0 at t = 0?
3. At which of the six number points does the particle have the smallest displacement if it started from x = 0 at t = 0?
4. If the particle started from x = 0 at t = 0, is its postion, x positive or negative when is moving in the -x direction?
   t, of nt 6 ts 1X le Figre 2-20 Question 5.
   

Answer 1

Slope of v - t ( v is velocity and t is time) graph give us the acceleration of the object. And the area under v - t curve gives us the displacement of the object.

(a) In the given curve we can see that at the point 1 and 4 the slope of the curve will be zero (because at these point the tangent will be parallel to the t - axis) . Hence at the points 1 and 4 particle has no acceleration.

(b) From the curve, we can see that the area under the curve at point 3 will be maximum if we starts from v =0 and t = 0 .

So, at point 3 particle will have greatest displacement.

(c) The area under the curve will be minimum at point 1 if we starts from v = 0 , t = 0 .

So, at point 1 , particle will have smallest displacement.

(d) As we can see that the area under the curve between points v =0 , t =0 (origin) to point 3 (positive area i.e. positive displacement) is very greater than the area under the curve between the points 3 and 5 (negative area i.e. negative displacement), Hence, we can conclude that the position of the particle will be positive when the velocity is in negative x - direction.

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