Help with maths questions?

Question

s = metres and t = time.
A) differentiate the formula to find the formula for velocity, can anyone show me how??
B What is the velocity after 2.5 seconds?

S= 1+30t-2t^2

Answer 1

s = 1 + 30t - 2t^2

velocity = ds/dt = 30 - 4t

v @ t=2.5 = 30 - (4 x 2.5) = 20 m/s

Answer 2

S= 1+30t-2t^2
dy/dx(differntiation)= Velocity
let v be the velocity
S= 1+30t^1-2t^2
v=u differentiate by multiplying the power of t to the number in front, and then take away 1 from the power of t.
If u can see there is no t in 1 in the S formular and it is a constant so it will go.

The 30t has the t to the power of 1, which is usually not written, so if the 1 is multiplied by 30 in front of the t it will still remain 30, and then the power 1 is taken away from one which gives 0, (1-1=0) so the t will go leaving only the 30.

The -2t^2 has a power of 2 which is multipled by the -2 in front of it and it gives -4, the 2 power is taken away from 1 and 1 remains (2-1=1), which makes the power 1

By doing this,
v=30-4t^1, which is the same thing as:
v=30-4t

when t is 2.5, the velocity v can be found by substituting the value ot t into the formular of v
v=30-4(2.5)
v=30-10
v=20seconds.

Answer 3

If you differentiate: S = 1+30t -2t^2 with respect to t you get:
v=velocity = dS/dt = 30 - 4t
Therefore, if you substitute 2.5secs for t in the equation for v you get the velocity at 2.5 seconds. i.e.:
v=30 - 4X2.5 =20 m/s . Threfore the ansver is: velocity is 20 m/s
20 metre per second). I hope this is helpful.

Answer 4

Sorry but i was a bit slow off the Markymark

s=1 + 30t - 2t^2

to differentiate (to find ds/dt)

ds/dt = 0 + 30 - 4t

so ds/dt = 30 - 4t

input t = 2.5
v = ds/dt
v = 30 - 4(2.5)
v = 30 - 10
v = 20 m/s

How do you get to this?

To deviate a formula:

e.g. (a) a = b^n

da/db = nb^n-1

make n = 2

a = b^2
da/db = 2b^ (2-1) = 2b^1
da/db = 2b

make n = 3
a = b^3
da/db = 3b^ (3-1) = 3b^2
da/db = 3b^2

e.g. (b) a = mb^n

da/db = nmb^n-1

make n = 2 and m = 3

a = 3b^2
da/db = (2*3)b^2-1 = 6b^1
da/db = 6b

i hope this helps.....

also if a number is contained in the equation with no nothing multiplying it .....it will differentiate to 0 always.

also in the equation if a number is multiplied by a variable (like t) it differentiates to the number i.e 30t becomes 30...i.e. 12t becomes 12....i.e. 67t becomes 67

and so on...

I hope this helps also.....

Answer 5

B) S= 1+30t-2t^2
Diff w.r.t to t
dS/dt = 30 -4t
put t=2.5 sec
V= 30 - 4 x 2.5

V=30-10= 20 m/s

Answer 6

d/dt s(t) = 30 - 4t

I could show this using limits, but the standard differential equation of a polynomial is easier:

If y = ax^n, dy/dx = nax^(n-1)

s(25) = 30 - 4(25) = -70

Answer 7

velocity= distance(s)/time

Answer 8

DIME BAR

Answer 9

Is there an echo in here...in here...in here...