# Kinematic Question

#### Harmony

I am currently studying Kinematic Chapter and I am facing problem in the following question:
The initial velocity of a particle is 15ms-1 along the Ox direction(Ox is a straight line). After 5.0 s its velocity is 15 ms-1 at an angle of 60 degree to the Ox direction. Find the magnitude and direction of the average acceleration of particles.

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#### Astronuc

Staff Emeritus
You have given an initial velocity and a direction, but you have not provided any information as to the forces, time or distance.

What is the coordinate system - Cartesian (x,y) where O would be origin, x is horizontal and y is vertical?

Is the projection in a gravitational field, e.g. earth's gravity field?

Is one considering or neglecting air resistance?

#### Harmony

Sorry, typing mistake. I have forgotten to include a sentence. The actual question is:
The initial velocity of a particle is 15ms-1 along the Ox direction(Ox is a straight line). After 5.0 s its velocity is 15 ms-1 at an angle of 60 degree to the Ox direction. Find the magnitude and direction of the average acceleration of particles.

Original post has been edited.

#### Doc Al

Mentor
The definition of average acceleration is:
$$\vec{a}_{ave} \equiv \Delta \vec{v} / \Delta t$$

#### Harmony

Well, the question has given me the time, which is 5 second. But i can't see any changes in speed, since initial velocity is same as the final velocity, only the direction is different. Should I consider different components of the velocity(after the direction has changed)?

#### Doc Al

Mentor
Velocity is a vector. The final speed is the same, but not the velocity.

Of course you must consider the components. Write the final and intial velocities in terms of their components. Then find the change in velocity: $$\Delta \vec{v} = \vec{v}_f - \vec{v}_i$$.

(Or you can solve it graphically.)

#### Harmony

Thanks for the advises. I have figured it out.

#### teng125

can you pls show the steps.i can't figure it out especially the velocities in terms of components.
thanx

#### Harmony

Actually,the initial velocity, the final velocity and the change of velocity form a vector triangle. You can use the vector diagram to solve the question, as every side of the vector triangle has the same magnitude.
So,the change of velocity will be 15ms-1,and the time taken will be 5 second. The acceleration=15ms-1/5s=3ms-2.
Unfortunately I don't know how to insert the vector diagram in my post.

One more thing: The change of velocity is equals to vector of the final velocity minus the vector of the initial velocity.

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