The position

The position of a body at any time T is given by the displacement function S=t³-2t²-4t-8. Find its acceleration at each instant time when the velocity is zero.

Correct answer:

a =  8

Step-by-step explanation:

$$\begin{gathered} s=t^3-2t^2-4t-8 \\ v=ds\mathrm{/}dt=3t^2-4t-4 \\ a=dv\mathrm{/}dt=6t-4 \\ v=0 \\ 3\ast t^2-4\ast t-4=0 \\ 3\cdot t^2-4\cdot t-4=0 \\ 3t^2-4t-4=0 \\ a=3;b=-4;c=-4 \\ D=b^2-4ac=4^2-4\cdot 3\cdot (-4)=64 \\ D>0 \\ {t}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{4\pm \sqrt{64}}{6}} \\ {t}_{1,2}={\displaystyle \frac{4\pm 8}{6}} \\ {t}_{1,2}=0.66666667\pm 1.33333333333 \\ {t}_1=2 \\ {t}_2=-0.666666666667 \\ \text{ Factored form of the equation: } \\ 3(t-2)(t+0.666666666667)=0 \\ t>0 \\ a=6\cdot t_1-4=6\cdot 2-4=8 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• A particle
  A particle moves in a straight line so that its velocity (m/s) at time t seconds is given by v(t) = 3t²-4t-4, t>0. Initially the particle is 8 meters to the right of a fixed origin. After how many seconds is the particle at the origin?
• Collision
  The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s², the second body has an initial speed of 6 m/s and an acceleration of 2 m/s². Fin
• Function 3
  Function f(x)=a(x-r)(x-s) the graph of the function has x- intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s.
• Acceleration
  The car accelerates at a rate of 0.5 m/s². How long travels 400 meters, and what will be its speed?
• Fall
  The body was thrown vertically upward at speed v₀ = 79 m/s. Body height versus time describes equation h = v₀ * t - (1)/(2) * 10 * t². What is the maximum height of body reach?
• Free fall
  Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s²
• Two cars
  Two cars, spaced d1 = 500 m apart, start moving against each other at time t1 = 0, the first car with acceleration a1 = 4 m/s ^ 2 and the second with acceleration a2 = 6 m/s ^ 2. At what time t2 do they meet? What distances s1 and s2 will they move from t
• Free fall
  The free fall body has gone 10m in the last 0.5s. Find the body speed at the moment of impact.
• Square ABCD
  Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
• Bomber
  The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s²)
• General line equations
  In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t
• Gravitation
  From the top of the 80m high tower, the body is thrown horizontally with an initial speed of 15 m/s. At what time and at what distance from the foot of the tower does the body hit the horizontal surface of the Earth? (use g = 10 ms-2)
• An acceleration
  The car goes on a straight road at a speed of 72 km/h. At some point, the driver starts to brake and stops the car in 5 seconds. Find: (a) the acceleration during braking (b) the distance traveled during braking.
• Driver
  The car driver drives at a speed of 100 km/h, saw the obstacle, and began to brake with a slowing of 5 m/s². What is the length of the pathway to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
• Train speed
  The train speed is decreased during 50 sec from 72 km/h to 36 km/h. Assuming that the train movement is equally slowing, find the the acceleration and the distance that it travels at.
• The body
  The body slides down an inclined plane forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s ^ 2. At what angle β must the plane be inclined so that the body slides on it
• G forces
  Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s²) occurs when a vehicle in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.