How do you calculate distance traveled from a speed/time acceleration graph?

Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distanc

4vir4ik [10]

The question is incomplete. Here is the complete question.

Cars A nad B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance $D_{A}$ beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed $v_{A}$ . Car B starts at the starting line but has a better engine than Car A and thus Car B travels at a constant speed $v_{B}$ , which is greater than $v_{A}$ .

Part A: How long after Car B started the race will Car B catch up with Car A? Express the time in terms of given quantities.

Part B: How far from Car B's starting line will the cars be when Car B passes Car A? Express your answer in terms of known quantities.

Answer: Part A: $t=\frac{D_{A}}{v_{B}-v_{A}}$

Part B: $x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$

Explanation: First, let's write an equation of motion for each car.

Both cars travels with constant speed. So, they are an uniform rectilinear motion and its position equation is of the form:

$x=x_{0}+vt$

where

$x_{0}$ is initial position

v is velocity

t is time

Car A started the race at a distance. So at t = 0, initial position is $D_{A}$ .

The equation will be:

$x_{A}=D_{A}+v_{A}t$

Car B started at the starting line. So, its equation is

$x_{B}=v_{B}t$

Part A: When they meet, both car are at "the same position":

$D_{A}+v_{A}t=v_{B}t$

$v_{B}t-v_{A}t=D_{A}$

$t(v_{B}-v_{A})=D_{A}$

$t=\frac{D_{A}}{v_{B}-v_{A}}$

Car B meet with Car A after $t=\frac{D_{A}}{v_{B}-v_{A}}$ units of time.

Part B: With the meeting time, we can determine the position they will be:

$x_{B}=v_{B}(\frac{D_{A}}{v_{B}-v_{A}} )$

$x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$

Since Car B started at the starting line, the distance Car B will be when it passes Car A is $x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$ units of distance.

5 0

2 years ago

Sound waves, water waves, and light waves are all alike in that they all

Paha777 [63]

Sound and water waves are longitudinal waves, they require a medium to travel through and occilate particles 90 degrees to the wave motion
Light is a transverse wave. It doesnt require a medium to travel through.
All three reflect, refract and diffract

Light is difficult to think of because it acts in ways which waves cannot explain in some cirumstances. It acts like a particle (called photons) in some conditions, but acts like a normal sound or water wave does in others. Try not to get too caught up in light being a wave or a particle because even physists dont know how to explain it yet.

7 0

3 years ago

A scooter travelling at 10 m/s speed up to 20 m/s in 4 sec. Find the acceleration of scooter.

Aleksandr-060686 [28]

Explanation:

The acceleration of the scooter is 2.5 m/s

3 0

3 years ago

How is the magnetic force on a particle moving in a magnetic field different from gravitational and electric forces.

harina [27]

Answer:

The magnetic force on a free moving charge depends on the velocity of the charge and the magnetic field, direction of the force is given by the right hand rule. While gravitational depends on the mass and distance of the moving particle and electric forces depends on the magnitude of the charge and distance of separation.

Explanation:

The magnetic force on a free moving charge depends on the velocity of the charge and the magnetic field and direction of the force is given by the right hand rule. While gravitational depends on the mass and distance of the moving particle and electric forces depends on the magnitude of the charge and distance of separation.

The magnetic force is given by the charge times the vector product of velocity and magnetic field. While gravitational force is given by the square of the particle mass divided by the square its distance of separation. Also electric forces is given by the square of the charge magnitude divided by the square its distance separation.

4 0

2 years ago

The slowest animal ever discovered was a crab found in the Red Sea. It traveled with an average speed of 5.70km/yr. how long wou

Vaselesa [24]

If it takes 1 year for this crab to travel 5,70km

Then, it will takes approximatly 1000/5,70 = 175 years to travel 1000 km

8 0

2 years ago

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