the particle's initial position is at t=0, x = 0 - 0 + 4 = 4m

velocity is rate of change of displacement = dx/dt = d(t^3 - 9t^2 +4)/dt
= 3t^2 - 18t

acceleration is rate of change of velocity = d(3t^2 -18t)/dt
= 6t - 18

the particle is stationary when velocity = 0, so 3t^2 - 18t =0
3t*(t - 6) = 0
t = 0 or t = 6s

acceleration = 6t - 18 = 0
t = 3s
at t = 3s, velocity = 3(3^2) -18*3 = -27m/s
displacement = 3^3 - 9*3^2 +4 = -50m

6 0

3 years ago

Read 2 more answers

The formula for the length of the hypotenuse in a right triangle is

kramer

Answer:

Step-by-step explanation:

3 0

4 years ago

A boat traveled 147 miles downstream and back. The trip downstream took 7 hours. The trip back took 21 hours. What is the speed

zimovet [89]

Answer:

The speed of current is 7 miles per hour

Step-by-step explanation:

Given as :

The distance cover by boat in downstream = D = 147 miles

The distance cover by boat in upstream = d = 147 miles

The time taken in downstream trip = T = 7 hours

The time taken in upstream trip = t = 21 hours

Let The speed of boat in still water = x mi/h

And The speed of current = y mi/h

The speed in downstream = S = (x + y) mi/h

The speed in upstream = s = (x - y) mi/h

Now, According to question

∵ Distance = speed × time

For downstream

D = S × T

Or, 147 miles = (x + y) mi/h × 7 hours

i.e 7 (x + y) = 147

Or, x + y = $\dfrac{147}{7}$

∴ x + y = 21 ........A

For upstream

d = s × t

Or, 147 miles = (x - y) mi/h × 21 hours

i.e 21 (x - y) = 147

Or, x - y = $\dfrac{147}{21}$

∴ x - y = 7 .......B

Now, Solving equations A and B

So, (x + y) + (x - y) = 21 + 7

Or, (x + x) + (y - y) = 28

Or, 2 x + 0 = 28

∴ x = $\dfrac{28}{2}$

i.e x = 14 miles per hour

The speed of boat in still water = x = 14 mi/h

Now, putting the value of x into eq B

So, y = x - 7

Or, y = 14 - 7

i.e y = 7 miles per hour

The speed of current = y = 7 mi/h

Hence, The speed of current is 7 miles per hour . Answer

7 0

3 years ago