Answer:
a) 23.51 m/s
b) 1.07 kg
Explanation:
Parameters given:
Kinetic energy, K = 295 J
Momentum, p = 25.1 kgm/s
a) The kinetic energy of a body is given as:
where m = mass of the body and v = speed of the body
We know that momentum is given as:
p = mv
Therefore:
K = 1/2 * pv
=> v = 2K / p
v = (2 * 295) / 25.1 = 23.51 m/s
The velocity of the body at that instant is 23.51 m/s.
b) Momentum is given as:
p = mv
=> m = p / v
m = 25.1 / 23.51 = 1.07 kg
The mass of the body at that instant is 1.07 kg
To understand this question, you need to understand the concept of acceleration first. Have you ever been in a car and noticed that it was getting faster and faster? That "speeding up" of the car is known as acceleration! Acceleration is essentially the rate at which you speed up.
Okay, so we now know what acceleration is. What are its units? The unit of acceleration is the change in velocity over a period of time:
If you haven't learned about velocity yet, just think about it as speed for now. The funny-looking triangle, ∆, is a symbol for "the change of." For example, if I started walking at 3 then sped up to 5
, then the change in my speed would be 2
, because I started walking 2
faster!
Okay, enough with all the explanations. Hopefully, you understand the units now. Let's take a look at the question. A car accelerates from 4 to 16
in 4 seconds. What would the acceleration be? Let's set up an equation:
a =
a is the acceleration, ∆v is the change in velocity, and t is the time elapsed.
Now, let's plug in our values! ∆v is the change in velocity, and to find that we simply have to subtract 16 by 4
. That makes sense, right? Back to the equation.
a =
a =
(16 - 4 is the change in velocity, and 4 is the number of seconds the car was accelerating)
a =
a = 3 ()
We have our answer! The car's acceleration is 3 meters per second^{2}.
(You might be thinking: Wait. Meters per second squared? The reason for that is because acceleration is the rate at which the speed increases! That makes the unit , which can be simplified down to
)
Let me know if you need clarification on anything I explained here!
- breezyツ