Assume a canister in a straight tube moves with a constant acceleration of -3 m/s2 and has a velocity of 13.5 m/s at t = 0.00 s.
(a) What is its velocity at t = 1.00 s?
v = m/s
(b) What is its velocity at t = 2.00 s?
v = m/s
(c) What is its velocity at t = 2.5 s?
v = m/s
(d) What is its velocity at t = 4.00 s?
v = m/s
(e) Describe the shape of a graph of velocity versus time for this parcel of air.
(f) What two things must be known at a given time to predict the canister's velocity at any later time?
I am lost here, I've been working on this for hours!
<< I've been working on this for hours! >>
During those hours, have you tried using the equation
V(t)= Vo + a*t ,
where Vo is the initial velocity and a is the acceleration rate?
I can help you with this physics problem! Let's go through it step by step.
To find the velocity of the canister at different times, 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
(a) To find the velocity at t = 1.00 s, we substitute the given values into the equation:
u = 13.5 m/s (given)
a = -3 m/s^2 (given)
t = 1.00 s
v = 13.5 m/s + (-3 m/s^2)(1.00 s)
v = 13.5 m/s - 3 m/s
v = 10.5 m/s
So, the velocity at t = 1.00 s is 10.5 m/s.
(b) To find the velocity at t = 2.00 s, we use the same equation:
u = 13.5 m/s (given)
a = -3 m/s^2 (given)
t = 2.00 s
v = 13.5 m/s + (-3 m/s^2)(2.00 s)
v = 13.5 m/s - 6 m/s
v = 7.5 m/s
So, the velocity at t = 2.00 s is 7.5 m/s.
(c) To find the velocity at t = 2.5 s, we again use the same equation:
u = 13.5 m/s (given)
a = -3 m/s^2 (given)
t = 2.5 s
v = 13.5 m/s + (-3 m/s^2)(2.5 s)
v = 13.5 m/s - 7.5 m/s
v = 6.0 m/s
So, the velocity at t = 2.5 s is 6.0 m/s.
(d) To find the velocity at t = 4.00 s, we use the equation:
u = 13.5 m/s (given)
a = -3 m/s^2 (given)
t = 4.00 s
v = 13.5 m/s + (-3 m/s^2)(4.00 s)
v = 13.5 m/s - 12 m/s
v = 1.5 m/s
So, the velocity at t = 4.00 s is 1.5 m/s.
(e) Describing the shape of the graph of velocity versus time:
Since the acceleration is negative (-3 m/s^2), the velocity will decrease over time if the initial velocity is positive. The graph will show a straight line sloping downwards with a negative slope.
(f) Two things that must be known at a given time to predict the canister's velocity at any later time are the initial velocity (u) and the acceleration (a). In this case, these values are given as u = 13.5 m/s and a = -3 m/s^2. With these two values, you can use the equation v = u + at to calculate the velocity at any desired time.
I hope this explanation helps you understand the problem better! Let me know if you have any further questions.