Kinematic Equations Homework Solutions

[alexandria]

Homework Statement

Homework Equations

relevant equations are listed with each question

The Attempt at a Solution

25. **

Displacement = 131 km (South)

Average velocity = total displacement / total time

Average velocity = 131 km (S) / 2.0 h

Average velocity = 65.5 km /h (south)


26. **

Given information:

v1 = 75 km/h

Convert to m/s:

(75 km/h) x (1000 m/1 km) x (1 h/3600 s) = 20.8 m/s

d = 42 m

total time = 3.4 s

a)

Calculate acceleration:

a = v2 – v1 / total time

a = 0 – 20.8 m/s / 3.4 s

a = -6.12 m/s2

Calculate distance:

total distance= v1(total time) + ½ a (total time)^2

= (20.8 m/s) x (3.4 s) – ½ (6.12 m/s2) x (3.4 s)2

= 35.35 m

Andrew traveled 35.35 m before stopping.b) ***

Andrew did not hit the fox.

42 m – 35.35 m = 6.65 m
c) ***

35.35 m / 4.2 m = 8.4 m

It took approx. 8 van lengths for Andrew to stop.


27. **

Given information:

v1 = 2.1 m/s (up)

total time = 3.0 s

acceleration = -9.81 m/s2 (down)

a)

Equation:

total displacement = v1(total time) + ½ a (total time)^2

Substitute and solve:

d = (2.1 m/s) x (3.0 s) – ½ (9.8 m/s2) x (3.0 s)^2

d = -37.8 = 37.8 m

Marian’s Balcony is 37.8 m high.

b)

v2^2 = v1^2 + 2a(total displacement)

= (2.1 m/s)2 + 2(-9.8 m/s2) x (-37.8 m)

= √746

= 27.3 m/s (down)

 

[haruspex]

That's all about right, but you could have used a shorter and more accurate path in 27 a) and b).
In a) do you know a SUVAT equation relating acceleration, time, initial speed and distance?
In b) do you know a SUVAT equatiom relating initial speed, final speed, time and acceleration?
(Using an intermediate result, as from 27a), as input to a further result often leads to loss of precision. E.g. while it might be appropriate to quote an intemediate result to 3 digits, you should use at least four as input to the next step.)

 

[alexandria]

can you explain what SUVAT equations are?

 

[haruspex]

can you explain what SUVAT equations are?

See e.g. http://www.thestudentroom.co.uk/wik...Equations_of_Motion_for_Constant_Acceleration.
The name comes from the five variables, s, u, v, a t. It is important to remember that these equations only apply when acceleration is constant throughout.

 

[alexandria]

so for questions 25, and 26 are they completely correct?
and when you say 'shorter and more accurate path to solve 27 a) and b)' do u mean that the answers are not as accurate as they should be? did i do it right or wrong?

 

[haruspex]

so for questions 25, and 26 are they completely correct?
and when you say 'shorter and more accurate path to solve 27 a) and b)' do u mean that the answers are not as accurate as they should be? did i do it right or wrong?

They could be a bit more accurate. 27b is out by about 1 percent, whereas quoting three significant figures here implies about 0.3% or better.
It's not a question of right or wrong. Using the best choice of equations from the SUVAT collection would have involved less working and produced more accurate answers.

 

[alexandria]

i see,
what about 25 and 26, i feel like I am missing something

 

[haruspex]

i see,
what about 25 and 26, i feel like I am missing something

Why? They look fine to me.

 

[alexandria]

ok thanks just clarifying