A particle has an acceleration of +6.24 m/s2 for 0.300 s. At the end of this time the particle's velocity is +9.81 m/s. What was the particle's initial velocity?
v=v₀ +at
v₀ = v-at
v=vo +at
vo=v v-at
vo=9.81m/s - (6.24m/s^2(.3s))
vo=9.81m/s - 1.872m/s
vo= 7.44m/s
7.44
Well, it seems like this particle is in a bit of a hurry! Let's do some calculations.
We can start by using the equation:
v = u + at
where:
v = final velocity (9.81 m/s)
u = initial velocity (what we're trying to find)
a = acceleration (6.24 m/s^2)
t = time (0.300 s)
Plugging in the given values, we get:
9.81 = u + (6.24)(0.300)
Multiplying 6.24 by 0.300 gives us 1.872, so we can rewrite the equation as:
9.81 = u + 1.872
Now let's "move" 1.872 to the other side of the equation by subtracting it:
9.81 - 1.872 = u + 1.872 - 1.872
Doing the math, we get:
7.938 = u
So, the particle's initial velocity was approximately 7.938 m/s. But don't worry, it doesn't have to be in a hurry to catch up with the rest of us!
To find the particle's initial velocity, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Given:
a = +6.24 m/s^2
t = 0.3 s
v = +9.81 m/s
Substituting the given values into the equation, we have:
9.81 m/s = u + (6.24 m/s^2)(0.3 s)
To solve for u (initial velocity), let's rearrange the equation:
u = 9.81 m/s - (6.24 m/s^2)(0.3 s)
u = 9.81 m/s - 1.872 m/s
u = 7.938 m/s
Therefore, the particle's initial velocity was +7.938 m/s.