The body is moving forward when v(t) > 0. Since you found the roots of v(t), it is easy to say for which t we have v(t) > 0.b) When is the body moving forward ? bakward ?
When a(t) > 0.c ) When is the body's velocity increasing ?
Q 1 )
Partical mothion At time t >= 0 the velcity of a body moving along the s-axis is v = t^2 - 4t + 3
a ) Find the body's acceleration each time the volicty is zero ?
b) When is the body moving forward ? bakward ?
c ) When is the body's velocity increasing ?
I solve a )
but about b an c ( How they solved )
a(t) v' = 2t - 4
t = 1 , t = 3
a (3) = 2 , a(1) = -2
what about b and c
The graph for v(t) is a parabola. Since the leading coefficient (i.e., 1) is positive, the branches are directed upward, i.e., when t is large (e.g., t = 1000), v(t) is positive. The roots are 1 and 3, so between 1 and 3 v(t) is negative, to the left of 1 and to the right of 3 v(t) is positive.
This is wrong because you are saying that the body moves both forward and backward when t > 2. Also, t > 3 is a special case of t > 2, so mentioning it explicitly is not necessary.t > 2 and t >3 = forward
t > 2 = backward
Most importantly, to find out if the body is moving forward or backward you are evaluating v'(t) = a(t), though post #2 above says that one needs to evaluate v(t) for this.
I am not sure how we can help since the question boils down to analyzing the properties of linear and quadratic functions, namely, when they are positive and negative. This is the topic for the Pre-Algebra and Algebra forums, or at most for Pre-Calculus. These topics come way before derivatives that you used in the OP.
I would recommend reviewing how to analyze signs of linear and quadratic functions and/or posting questions in the forums above. If you have concrete questions about the hints given in this topic, feel free to ask those here as well.
You are begging and bumping both of which are strictly against the rules.
You know that this is not a homework service nor is it a tutorial service.
We have no obligation to give you answers, particularly have been given a complete solution to this question.
Look at reply #2. That is all you need to work this question. If you do not understand, the you need a live tutor. We will not do that.