# An object is at rest at #(2 ,8 ,6 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,5 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

The time is

By signing up, you agree to our Terms of Service and Privacy Policy

Using the formula ( d = ut + \frac{1}{2}at^2 ), where ( d ) is the displacement, ( u ) is the initial velocity (which is 0 since the object is at rest), ( a ) is the acceleration, and ( t ) is the time taken:

( d = \sqrt{(7-2)^2 + (5-8)^2 + (3-6)^2} )

( a = \frac{5}{3} ) m/s(^2)

Solve for ( t ) using the given formula.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the time it takes for the object to reach point B, we can use the kinematic equation:

[ d = v_i t + \frac{1}{2} a t^2 ]

Where:

- ( d ) is the displacement,
- ( v_i ) is the initial velocity,
- ( a ) is the constant acceleration, and
- ( t ) is the time taken.

Given that the object is at rest initially (( v_i = 0 )), and the acceleration is ( 5/3 ) m/s², and the displacement is the distance between the initial position and point B, we can plug in the values to find ( t ).

The displacement ( d ) between the points can be calculated using the distance formula in three dimensions:

[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} ]

Given the coordinates of the points A and B, we can calculate the displacement ( d ). Then, we can use the displacement and the given acceleration to solve for ( t ) using the kinematic equation.

Substituting the values into the equation, we solve for ( t ) to find the time it takes for the object to reach point B.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- If an object with uniform acceleration (or deceleration) has a speed of #3 m/s# at #t=0# and moves a total of 8 m by #t=4#, what was the object's rate of acceleration?
- The position of an object moving along a line is given by #p(t) = 4t - sin(( pi )/4t) #. What is the speed of the object at #t = 1 #?
- What is the acceleration experienced by a car that takes 10 s to reach 27 m/s from rest?
- A bicyclist moving at a constant speed takes 10.0 seconds to travel 500 meters down a path inclined 30.0" downward from the horizontal. What is the vertical velocity of this motion?
- A projectile is shot from the ground at a velocity of #52 m/s# and at an angle of #(pi)/2#. How long will it take for the projectile to land?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7