Understanding Acceleration and Motion with a Constant Acceleration Formula

In summary, the given formula for acceleration is a=B√t, where B=1.25 with appropriate units. The dimensions of B can be expressed in terms of M L and T (mass, length, and time). The speed can be found as a function of time by relating it to acceleration. The position can be found as a function of time by relating it to speed. At t=6.75s, the acceleration, speed, and position can be calculated. Additionally, the average speed for the time interval t=0s to t=6.75s can also be found. To solve this problem, start by determining the units of B and how speed and distance are related to acceleration and speed, respectively.
  • #1
demv18
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Homework Statement


the acceleration of a particle is given by a=B√t where B=1.25, with the appropriate units. At t=0s, v=7m/s and x=1.5m

a) what are the dimensions for "B" appearing in the formula a=B√t ?

b) what is the speed as a function of time?

c) What is the position as a function of time?

d) what are the acceleration, speed, and position at t=6.75s?

e) what is the average speed for the time interval t=0s to t=6.75s?

Really need a quick explanation of this problem... no idea where to start!


Homework Equations


i have no idea :(


The Attempt at a Solution

 
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  • #2
Welcome to PF. Sometimes the difficulty is just getting started.

a. "dimensions" is this context, is related to the units - work out the units of B, then express them in terms of M L and T (mass, length and time).

b. how is speed related to acceleration?

c. how is distance related to speed

d & e come from the last answers.
 

What is acceleration?

Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both magnitude and direction. In simpler terms, it measures how quickly the velocity of an object is changing.

How is acceleration calculated?

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

What is the difference between average and instantaneous acceleration?

Average acceleration is the change in velocity over a specific interval of time, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated using the change in velocity over the entire interval, while instantaneous acceleration requires finding the slope of the velocity-time graph at a specific point.

How does acceleration affect an object's motion?

Acceleration can cause an object to change its speed, direction, or both. If an object has a positive acceleration, it is speeding up, while a negative acceleration (also known as deceleration or retardation) causes the object to slow down. If the acceleration is zero, the object maintains a constant velocity.

What factors affect the acceleration of a particle?

The acceleration of a particle can be affected by several factors, including the force acting on the particle, the mass of the particle, and the direction of the force relative to the direction of motion. Other factors such as friction and air resistance can also affect the acceleration of a particle.

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