Velocity and Displacement: How to Derive Expressions from Acceleration Equation

In summary, to derive expressions for velocity and displacement of a car with an acceleration of a=18t - 4 ms^-2 and initial velocity and displacement of 0, start with the definition of acceleration as the rate of change of velocity. Replace 'a' with 'dv/dt' in the equation to find 'v'.
  • #1
BonBon101
5
0

Homework Statement



The acceleration a ms^-2 of a car is given by a=18t - 4 where t is the time in seconds.Derive expressions for the velocity v ms^-1 and the displacement x m if the initial velocity and displacement are both zero

Homework Equations





The Attempt at a Solution


would really appreciate any help with this.I have no idea where to start!Trying to get a sample answer so i can study it to past exam paper questions
 
Physics news on Phys.org
  • #2
Start with the definition of acceleration:

acceleration is the rate of change of velocity, so a= dv/dt.

If you replace 'a' by 'dv/dt' in your equation, can you find 'v'?
 

FAQ: Velocity and Displacement: How to Derive Expressions from Acceleration Equation

What is the difference between velocity and displacement?

Velocity is a vector quantity that measures the rate of change of an object's position with respect to time, including both direction and magnitude. Displacement, on the other hand, is a vector quantity that measures the change in an object's position from its starting point to its end point, without considering the path taken. In other words, velocity is the rate of change of displacement.

How do you calculate velocity?

Velocity is calculated by dividing the change in an object's position (displacement) by the change in time. Mathematically, it is expressed as v = Δx/Δt, where v is velocity, Δx is change in position, and Δt is change in time.

What is the difference between average velocity and instantaneous velocity?

Average velocity is the average rate of change of an object's position over a given interval of time, while instantaneous velocity is the velocity of an object at a specific moment in time. In other words, average velocity considers the entire interval, while instantaneous velocity only considers a specific point within the interval.

How does velocity affect displacement?

Velocity affects displacement by determining the direction and magnitude of the object's movement. If the velocity is constant, then the displacement will be directly proportional to the velocity. However, if the velocity is changing, then the displacement will also be affected by the acceleration or deceleration of the object.

What units are used to measure velocity and displacement?

Velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h), while displacement is measured in meters (m) or kilometers (km). However, other units such as miles per hour (mph) or feet per second (ft/s) may also be used depending on the context and preference of the scientist.

Back
Top