A few simple questions~ (1 Viewer)

[Follz21]

Hey all

Just wondering if you could help me answer some of these annoyingly simple questions:

1a) Find the final velocity of a vehicle moving initially at 15ms-1 and subject to a deceleration of -0.5ms-2 for 40s

(is it -5ms-1?)

1b)Find the average velocity of the vehicle over this duration, and the time at which value this corresponds to it's instantaneous velocity.

2a)Show from the basic equations for acceleration and average velocity that the total displacement of an object is given by:

r= ut + 1/2 at^2

(r= displacement)

2b) Show that, only if the initial velocity is zero, the time taken for an accelerating object to travel a given distance is given by:

t= [sqroot 2r/a]


Thanks for any help, I greatly appreciate it.

 

[darkchild69]

1a) Find the final velocity of a vehicle moving initially at 15ms-1 and subject to a deceleration of -0.5ms-2 for 40s

v = u + at
v = 15 + (-0.5*40)
v = 15 - 20
v = -5 ms^-1


1b)Find the average velocity of the vehicle over this duration, and the time at which value this corresponds to it's instantaneous velocity.

vav = (v + u)/2
= (15 - 5) / 2
vav = 5ms^-1

t = (v-u)/a

t = (5 - 15) /-0.5

t = 20s


2a)Show from the basic equations for acceleration and average velocity that the total displacement of an object is given by:

v = u + at

av velocity = ((v+u)/2) = r/t

r = ((v+u)/2)t
r = vt/2 + ut/2
r = (u+at)t/2 + ut/2
r = (ut)/2 + (at^2)/2 + (ut)/2
r = ut + (at^2)/2


2b) Show that, only if the initial velocity is zero, the time taken for an accelerating object to travel a given distance is given by:

r = ut + (at^2)/2

if u = 0 then

r = (at^2)/2

2r/a = t^2

t = (2r/a)^1/2




Thanks for any help, I greatly appreciate it.

No probs

 

[khorne]

beaten:

1)a)

We have:

u = 15
a = -0.5
t = 40
v = ?

So we use the formula:

v = u + at

v = 15 + (-0.5)(40)

v = 15 - 20

v = -5m/s

1)b)

Average velocity = u+v/2 = 15 + (-5)/2 = 10/2 = 5m/s

As for the time taken when it's 5m/s, let v = 5, u = 15, a = -0.5

t = 5-15/-0.5
t= -10/-0.5
t= 20

2)a) a = v-u/t

therefore v = u + at

Average velocity = u+v/2 = r/t

therefore r = [u+v/2]t

so take this, and sub v = u + at in for v

r = 2ut + at^2/2

r = ut + 0.5at^2

2)b) r = ut + 0.5at^2

If u = 0, ut = 0

thus r = 0.5at^2

so 2r = at^2

2r/a = t^2

t = sqrt[2r/a]

Otherwise, if the initial velocity isn't zero, you would have an extra term.

 

[Follz21]

Thanks fellas. Really appreciate the help!