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:

$X=V.t$

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

$X=0.93 km$