Solving Acceleration Problem for Velocity and Distance

In summary, acceleration is the rate of change in an object's velocity over time, measured in meters per second squared (m/s²). It can be calculated by dividing the change in velocity by the change in time. The relationship between acceleration, velocity, and distance is that when acceleration increases, velocity increases at a faster rate, leading to a greater distance traveled. There are two types of acceleration: average and instantaneous. Average acceleration is the overall change in velocity over a given time period, while instantaneous acceleration is the change in velocity at a specific moment. To solve for velocity and distance when given acceleration, you can use the equations vf = vi + at and d = vit + 1/2at². These equations take into account the
  • #1
sapiental
118
0
A particle moves with acceleration a(t) = cos(t)+3

Intital velocity v(0)= 5
initial position s(0) =3

a) fin velocity of particle at time t

v(t) = sin(t)+3t+C
plugging 0 for t I get C = 5

s(t) = -cos(t) + 3/2t^2 + 5t + C
plugging 0 for s I get C = 3

answer: v(t) = sin(t)+3t+5

b) What is the total distance traveled from t = pi to t = 2pi

integral pi to 2pi = v(t) = sin(t)+3t+5
= s(2pi)-s(pi)


Thanks!
 
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  • #2
I think the "C" in the x(t) is 4 and not 3.

[itex]\cos 0=1 [/itex]

Daniel.
 

FAQ: Solving Acceleration Problem for Velocity and Distance

What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is commonly measured in meters per second squared (m/s²).

How do you calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula is: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the relationship between acceleration, velocity, and distance?

Acceleration is directly related to velocity and indirectly related to distance. When acceleration increases, velocity increases at a faster rate, causing an object to travel a greater distance in a given amount of time.

What is the difference between average acceleration and instantaneous acceleration?

Average acceleration is the overall change in velocity over a given period of time, while instantaneous acceleration is the change in velocity at a specific moment in time. Average acceleration is calculated using the final and initial velocities, while instantaneous acceleration is calculated using the derivative of the velocity-time graph.

How do you solve for velocity and distance when given acceleration?

To solve for velocity and distance, you can use the equations: vf = vi + at and d = vit + 1/2at². These equations take into account the initial and final velocities, acceleration, and time to calculate the velocity and distance of an object.

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