Starting at rest, a car has an acceleration given by: a=3t2-1. How far is the car...

Starting at rest, a car has an acceleration given by: a=3t²-1. How far is the car after 4 seconds? Consider starting position as zero. Be sure to include the units of measure. Use for gravity acceleration the value of 10. Do not use rounded numbers in the results.

I will like your answer if the work makes sense. If not, I will comment on it.

Expert Solution

The given function is acceleration. So to find the distance covered you need to integrate that function twice. After first integration you will get velocity and after second integration you get the required distance.

Then put t=4 sec then you get you required distance covered.

I have done it below. Hope you will understand.

Note :- No unit is used in the question for the acceleration "a" but the gravitational acceleration is given in the value of 10 m/s². That is why I use the unit of "x" in "meter". And obviously time "t" is in sec(given).

genius_generous answered 2 years ago

A car is traveling down the expressway at 31.7 ? with no acceleration. How far has...

A car is traveling down the expressway at 31.7 ? with no acceleration. How far has the car? traveled in 3.9 hours? If the speed limit in such expressway is 70mph, should the driver receive a speed ticket? A car is traveling down the same expressway as in the previous problem, it is traveling at 22.3 7 ?. If it constantly accelerates at a rate of 4.3 ?, in how many minutes is it going to pass the speed limit.

A computer disk drive is turned on starting from rest and has constant angular acceleration. Part...

A computer disk drive is turned on starting from rest and has constant angular acceleration. Part A If it took 0.420 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution? Part B What is its angular acceleration, in rad/s2?

A wheel, starting from rest, has a constant angular acceleration of 0.1 rad/s2. In a 2.4-s...

A wheel, starting from rest, has a constant angular acceleration of 0.1 rad/s2. In a 2.4-s interval, it turns through an angle of 120 rad. How long has the wheel been in motion at the start of this 2.4-s interval?

A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It...

A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back to Earth. (a) Find the rocket’s height when it runs out of fuel; (b) find the rocket’s velocity when it runs out of fuel; (c) find the maximum height the rocket reaches; (d) find the rocket’s velocity the instant before the rocket...

A wheel, starting from rest, rotates with a constant angular acceleration of 1.40 rad/s2. During a...

A wheel, starting from rest, rotates with a constant angular acceleration of 1.40 rad/s2. During a certain 6.00 s interval, it turns through 36.6 rad. (a) How long had the wheel been turning before the start of the 6.00 s interval? (b) What was the angular velocity of the wheel at the start of the 6.00 s interval?

A bicyclist starting at rest produces a constant angular acceleration of 1.6 rad/s^2 for wheels that...

A bicyclist starting at rest produces a constant angular acceleration of 1.6 rad/s^2 for wheels that are 38 cm in radius. What is the bicycles linear acceleration? What is the angular speed of the wheels when the bicyclist reaches 11m/s? How many radians have the wheels turned through in that time? How far has the bicycle traveled?

A car starts from rest and travels east with an acceleration of 4x10^-3 m/s^2. Another car...

A car starts from rest and travels east with an acceleration of 4x10^-3 m/s^2. Another car travels towards west at a constant speed of 70kph. The two cars are 100km apart. a. What is the time it takes for the two cars to meet b. time it takes for them to be 100km apart for the second time

A Ferris Wheel, starting from rest, undergoes a constant angular acceleration of 0.033 rad/s2 to get...

A Ferris Wheel, starting from rest, undergoes a constant angular acceleration of 0.033 rad/s2 to get to its final operating angular velocity of 0.24 rad/s. (a) How long does it take the Ferris Wheel to get to its operating angular velocity? (b) How many revolutions does it make during this time interval?

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 4.00...

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 4.00 s, it rotates 13.2 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 4.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 4.00 s?

A test rocket is launched, starting on the ground, from rest, by accelerating it along an incline with constant acceleration "a". The incline ha

A test rocket is launched, starting on the ground, from rest, by accelerating it along an incline with constant acceleration "a". The incline has length "L", and it rises at ? degrees above the horizontal. At the instant the rocket leaves the incline, its engines turn off and it is subject only to gravity, g?+9.81m/s2. (Air resistance can be ignored). Taking the usual x-y coordinate system, with an origin at the top edge of the incline, (a)what is the position vector when the rocket is at its highest point? (b)What is the position vector when the rocket is on its way back down and once again at the same height as the top edge of the incline? Your symbolic answer should only depend on a, L,?, g, and/or numerical factors Asked by

Question