An object is at rest at #(1 ,2 ,9 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(6 ,1 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
The time is
Apply the equation of motion
Therefore,
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:
[ \Delta d = v_0 t + \frac{1}{2} a t^2 ]
Where:
- ( \Delta d ) is the displacement (change in position), which is the distance between the initial and final points.
- ( v_0 ) is the initial velocity, which is zero since the object is at rest.
- ( a ) is the constant acceleration.
- ( t ) is the time.
Given:
- Initial position ( P_1(1, 2, 9) )
- Final position ( P_2(6, 1, 3) )
- Acceleration ( a = 1 , m/s^2 )
The displacement ( \Delta d ) can be calculated using the distance formula:
[ \Delta d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} ]
Substituting the values:
[ \Delta d = \sqrt{(6 - 1)^2 + (1 - 2)^2 + (3 - 9)^2} ] [ \Delta d = \sqrt{25 + 1 + 36} ] [ \Delta d = \sqrt{62} ]
Now, we can rearrange the kinematic equation to solve for time:
[ t = \frac{-v_0 \pm \sqrt{(v_0)^2 + 2a \Delta d}}{a} ]
Since ( v_0 = 0 ), this simplifies to:
[ t = \frac{\sqrt{2\Delta d}}{a} ]
Substitute the values:
[ t = \frac{\sqrt{2 \times \sqrt{62}}}{1} ] [ t = \sqrt{2 \times \sqrt{62}} ]
Calculating the value:
[ t \approx \sqrt{2 \times 7.874} ] [ t \approx \sqrt{15.748} ] [ t \approx 3.97 , \text{seconds} ]
So, it will take approximately 3.97 seconds 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.
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.
- An object travels North at #7 m/s# for #9 s# and then travels South at #6 m/s# for # 7 s#. What are the object's average speed and velocity?
- What is the weight (on earth) of a 13.5-gram object?
- What are some examples of scalar numbers?
- How do you find acceleration from velocity?
- A brand new Rolls-Royce rolls off the back of a truck as it is beling delivered to tis owner. Full question in details?

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