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In-s [12.5K]
3 years ago
12

The position of a particle is given by the function x=(5t3−8t2+12)m, where t is in s. at what time does the particle reach its m

inimum velocity?

Physics
2 answers:
Lady_Fox [76]3 years ago
8 0

The particle reach its minimum velocity at time 1.06 sec.

The function is given as

x=5t^3-8t^2+12

Differentiating the above equation with respect to time, to obtain the velocity

dx/dt=v=15t^2-16t

For maximum and minimum values, put dx/dt=0

15t^2-16t=0

On solving the equation, t=0, 1.06

Therefore at time t=1.06 sec, the particle has the minimum value of velocity.


Stella [2.4K]3 years ago
8 0

The particle reaches its minimum velocity at t = 0 s or t = 16/15 s

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

\large {\boxed {a = \frac{v - u}{t} } }

\large {\boxed {d = \frac{v + u}{2}~t } }

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem!

<u>Given:</u>

x = ( 5t^3 - 8t^2 + 12) ~ m

To find the velocity function, we will derive the position function above.

v = \frac{dx}{dt}

v = 5(3)t^{3-1} - 8(2)t^{2-1}

v = ( 15t^2 - 16t ) ~ m/s

Next to calculate the time to reach its minimum speed, then v = 0 m/s

0 = ( 15t^2 - 16t )

0 = t( 15t - 16)

\large {\boxed {t = 0 ~s ~ or ~ t = 16/15 ~ s} }

<h3>Learn more</h3>
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

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SOMEONE PLEASE HELP ME ASAP PLEASE!!!!!​
Zina [86]

Answer:

x₁ = 58.09 m

Explanation:

Displacement is calculated by finding the final distance away from a point then subtracting the initial distance.

Given that initial position of object is x=25.89 m

Displacement Δx=32.2 m

Final position x₁=?

Δx = x₁-x

32.2= x₁-25.89

32.2+25.89 = x₁

58.09 m =x₁

5 0
3 years ago
Two forces that make up 3rd law of motion can: 1)Act on the same object 2)do not act on same time 3)Act on different objects 4)D
Ede4ka [16]

Answer:

3) Act on different objects

Explanation:

Newton's third law of motion states that for every action there is an equal and opposite reaction.

Action-reaction force pairs make it possible for fishes to swim, birds to fly, cars to move, etc.

Basically, action-reaction force pairs are characterized by the following statements;

I. The forces are the same type such as magnetic force, contact force or gravitational force.

II. The forces are equal in magnitude but opposite in direction.

III. They act up on two different bodies.

Hence, the two forces that make up 3rd law of motion can act on different objects.

For example, while driving down the road, a bug strikes the windshield of a vehicle (Action) and makes a quite obvious mess in front of the face of the driver of the vehicle (Reaction) i.e the bug hit the vehicle and the vehicle hits the bug.

5 0
3 years ago
How does the speed ratio change as you switch between different gears on a bicycle, and how does this affect the force you need
FromTheMoon [43]

An average cyclist generates about 183 watts while doing 19 mph or 30.4 kph. Power = force × velocity. Force of a pedalling applied by a human for achieving 30.4 kph = 183/8.44 = 21.68 newtons. This is for upright bicycles.

7 0
3 years ago
What is the transfer of energy to a system by the application of a force called?
pav-90 [236]
It is called Work done
6 0
4 years ago
1. The smallest shift you can reliably measure on the screen is about 0.2 grid units. This shift corresponds to the precision of
nadya68 [22]

Answer:

Explanation:

each grid corresponding  0.1s⁻¹.

0.2grid unit = 0.2×0.1 =0.02s⁻¹

distance of the star from telescope

d = 1/p

d= 1/0.02= 50 par sec

1par sec = 3.26 light year

1 light year = 9.5×10¹²km

3.26ly=3.084×10¹³km

d= 50×3.084×10¹³=1.55×10¹⁵km

5 0
3 years ago
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