1. ## help with question

I have a question that i dont know where to start

An object its travelling along the x-axis so that its speed is given by
v(t)=t^2 -7t +10 m/s
A) find the times when the object is at rest.
B)Find the acceleration at both of these times. Interperate the acceleration in terms of the motion of the object.
C) if the object its at x=0m at t=1, find the position of the object at time t.
D)find the leftmost position of the object for all t>or=0

Any help would be great to push me in the right direction
Thanks
Jimmy

2. Originally Posted by jimmy12345
I have a question that i dont know where to start

An object its travelling along the x-axis so that its speed is given by
v(t)=t^2 -7t +10 m/s
A) find the times when the object is at rest.
B)Find the acceleration at both of these times. Interperate the acceleration in terms of the motion of the object.
C) if the object its at x=0m at t=1, find the position of the object at time t.
D)find the leftmost position of the object for all t>or=0

Any help would be great to push me in the right direction
Thanks
Jimmy
Hi jimmy12345.

A) Set $\displaystyle v(t)=0$ and solve for $\displaystyle t.$

B) The acceleration is $\displaystyle a(t)=v'(t).$ Substitute the values of $\displaystyle t$ you found in (A) into this. The accleration is positive if its speed is increasing.

C) The displacement is $\displaystyle x(t)=\int v(t)\,dt.$ Substitute $\displaystyle x(1)=0$ to find the constant of integration.

D) If you sketch the curve of $\displaystyle x(t)$ against $\displaystyle t$, you should find that the minimum displacement of the object is at $\displaystyle t=0.$

PS: I rather think they want you to find the leftmost position of the object for $\displaystyle t\ge\color{red}1$ (not 0). In this case, use the results you found in (A) and (B) to find the minimum value of $\displaystyle x(t)$ for $\displaystyle t\ge1$ (it would be at the time when the velocity is zero and the acceleration is positive).