Kinematics - particle acceleration and distance travelled

In summary, the problem involves a particle with an initial velocity of 10 m/s that changes direction and ends up with a velocity of 20 m/s in the opposite direction. With an acceleration of -10 m/s2, the particle travels a total distance of either 15 m, 20 m, 25 m, or 30 m. Using the equations for average velocity and final velocity, the correct answer can be calculated to be 25 m.
  • #1
GoGoGadget
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Kinematics -- particle acceleration and distance travelled

Homework Statement


A particle moving at 10 m/s reverses its direction to move at 20 m/s in the opposite direction. If its acceleration is -10 m/s2, what is the total distance that it travels?

A) 15 m

B) 20 m

C) 25 m

D) 30 m

Homework Equations


a = Δv/t

v = Δx/t




The Attempt at a Solution



In one direction:

time = velocity/acceleration = 10/10 = 1 s

velocity = distance/time = velocity * time = distance

distance = 10 m/s * 1s = 10 m

In the reverse direction:

acceleration = velocity/accelertion; time = velocity/acceleration

time = 20 m/s/10 m/s2 = 2 s

velocity = distance/time; distance = velocity * time = 20 m/s * 2 = 40 m

Distance traveled:

40 m + 10 m =50 m

I realize my final answer did not come out to be any of the choices above but am not sure of any other correct way to approach this problem.
 
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  • #2
Hello.

Your results for the two times look good.

The equation Δx/t (or Δx/Δt) is the formula for average velocity vavg.

So, Δx = vavg Δt.

What are the average velocities for the first and second parts?
 
  • #3
I would use the Kinematic equations, in particular x = V_o(t) + 1/2 at^2 and V_f = V_o + at. The first equation gives you the distance traveled, once you know the time, which is calculable from the other equation. Using this, the answer comes out as one of the choices you listed. This form of the equations is a little easier to work with in my opinion.
 

Related to Kinematics - particle acceleration and distance travelled

What is Kinematics?

Kinematics is the study of motion, including the description of the positions, velocities, and accelerations of objects without considering the forces that cause the motion.

What is particle acceleration?

Particle acceleration is the rate at which the velocity of a particle changes over time. It is measured in units of distance per unit time squared, such as meters per second squared (m/s^2).

How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is Δv/Δt, where Δv represents the change in velocity and Δt represents the change in time.

What is distance travelled?

Distance travelled is the total length of the path an object has taken, regardless of direction. It is a scalar quantity, meaning it only has magnitude and no direction.

How is distance travelled calculated?

Distance travelled can be calculated by multiplying the average velocity by the total time travelled. The formula for distance travelled is d = vavg * t, where d represents distance, vavg represents average velocity, and t represents time.

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