Constant accleration problem

[Tipolymer44]

Homework Statement

I need help on this homework problem I can't seem to figure it out.
A objects constant acceleration is north at 40 m/s^2. At time 0 its velocity vector is 15 m/s west at what time will the magnitude of the velocity be 30 m/s?

Homework Equations

This is the eq i used: delta T =(Vf-Vi)/a
I set Ti as 0.

The Attempt at a Solution

So I got 30-15/40= .375 secs

I also tried subtracting gravity from acceleration to give (30-15)/(40-9.8) =.496 secs

These are apparently wrong. what should i be doing?

 

[quietrain]

there is direction involved here so you cannot just pluck values into a formula

so the question nicely sets north (y-axis) and west (x-axis) for you.

so question wants the time when the MAGNITUDE of velocity is 30m/s, which means your x and y components of the velocity, will have to give you a resultant of 30m/s

notice your x-component velocity of 15m/s doesn't change since there is no acceleration in this direction, acceleration is only towards north (y-axis)

so in order to find the y-component velocity THAT will give you 30m/s resultant velocity, you have to use Pythagorean theorem as it is a triangle. draw it out and you will see

so its 30² = 15² + y², where y is your velocity in y-axis direction

so solving, y = 26m/s

so now you use your formula ALONG THE Y-direction

time taken = { v_{f,along y-axis} - v_{i, along y-axis} } / a _{along y-axis}
which is

(26 - 0) / 40 = 0.65s , the initial velocity is 0 because the object is moving west, there is no y-direction velocity

 

[Tipolymer44]

ahhh, so i basically need to formulate the directional components before i can solve for t

 

[quietrain]

yes.

 

[rwisz]

To solve this problem, you need to use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 30 m/s, the initial velocity is 15 m/s, and the acceleration is 40 m/s^2. Plugging these values into the equation, we get:

30 m/s = 15 m/s + (40 m/s^2)t

Solving for t, we get t = 0.375 seconds. So your first attempt was correct.

Your second attempt using gravity is incorrect because the problem does not mention anything about gravity. The acceleration given is only in the north direction.

In general, when solving problems involving constant acceleration, it is important to pay attention to the units and directions involved and use the appropriate equations. I hope this helps!