Question

A car is moving on a straight road in a fixed direction at a constant speed of v = 62 km/h with respect to the road. You wish to state the kinematic vectors of the motion of the car by using a Cartesian coordinate system whose positive x-axis is pointed in the direction of the motion of the car and the origin is fixed at some point on the road. A. What is the expression for the velocity of the car, using the speed v and the unit vectors i,j, and k?

B. What is the x-component of the position vector, in units of kilometers, at time t=0.015 hr?

Answer 1

Answer:

A) $V=62 i + 0 j + 0 k$

B) $X=0.93 km$

Explanation:

A) In this situation we are talking about a car moving only in the X- axis, hence the velocity of the car is:

$V=62 i + 0 j + 0 k$

Where the unit vectors $i$, $j$ and $k$ represent the components $x$, $y$ and $z$ in the cartesian plane.

In this sense, each unit vector is defined to have a magnitude of exactly one (1).

B) Velocity is defined as the variation of position in time, if this car is moving only along the x direction we will have:

$V=\frac{X}{t}$

Clearing the position:

$X=V.t$

$X=(62 km/h)(0.015 h)$

$X=0.93 km$

Answer 2

The distance travelled by a object is the product of its velocity and the time taken to cover the distance.

• A)The expression for the velocity of the car, using the speed v and the unit vectors i ,j, and k is,

         $V=62\hat i+0\hat j+0\hat k$.

• B)The x-component of the position vector, in units of kilometers, at time t=0.015 hr is 0.93 km.

What is constant speed?

Constant speed is the speed by which a body travelled same distance for each interval of time.

Given information-

The constant speed of the car is 62 km/h.

Positive x-axis is pointed in the direction of the motion of the car.

The origin is fixed at some point on the road.

• A) The expression for the velocity of the car, using the speed v and the unit vectors i ,j, and k-

The constant speed of the car is 62 km/h in x-axis

As the car is moving in he x-axis direction of the Cartesian coordinate system. Thus the y-axis and z-axis are zero.

The expression can be given as,

$V=62\hat i+0\hat j+0\hat k$

Here, $\hat i ,\hat j, \hat k$ are the components as unit vector of the $x,y,z$ in respectively in the Cartesian coordinate system.

• B) The x-component of the position vector, in units of kilometers, at time t=0.015 hr

The distance travelled by a object is the product of its velocity and the time taken to cover the distance.

Here the velocity of the body is 62 km/h and time is 0.0015 hr. Thus the distance travelled can be given as,

$x=62\times0.015\\x=0.93\rm km$

Hence,

• A)The expression for the velocity of the car, using the speed v and the unit vectors i ,j, and k is,

         $V=62\hat i+0\hat j+0\hat k$.

• B)The x-component of the position vector, in units of kilometers, at time t=0.015 hr is 0.93 km.

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