I'm currently working on a problem in which an object's speed remains the same, but it experiences a change in direction after some time. I'm fairly sure it experiences an acceleration in order to change direction.
However, I am confused because of the change in direction.
I want to use the formula $A_x = \Delta v / \Delta t $. Since the object experiences a change in direction at some point but still travels at the same speed, would the second velocity technically be negative? Like so:
$V_1$ = 5.0m/s
,$V_2$ = 5.0m/s,
$T_1$ = 0 seconds, $T_2$ = 10 seconds
$A_x = V_1 – (-V_2) / T_1 – T_2 $
Also, does it matter which direction? Would it be the same as travelling right and then turning left/right/around?
Best Answer
Yes, any change in velocity means an acceleration has occurred. That includes a change in direction of the velocity.
If the first velocity is in the positive direction, yes the second might be negative. Is this a 1-dimensional problem?
That will give you the average acceleration over the total time. It tells you nothing about the instantaneous acceleration at any specific time. Also, for $A_x$ you would use $\Delta v_x$.
Any curvilinear motion (which can't happen in 1-D motion) requires a sideways acceleration component of $$ a_{\perp} = \frac{v^2}{r} $$ where $v$ is the instantaneous speed and $r$ is the instantaneous radius of curvature.