How do you find Acceleration when given Distance and Time?

In summary, the question asks for the acceleration of a dragster from the 20.0m mark to the 400.0m mark. Using the equation v=d/t, the initial velocity is found to be 21.16 m/s. However, to find the final velocity and the correct acceleration, the equation d=\frac{Vo+Vf}{2}t should be used. This gives the final velocity as 0 m/s and the acceleration as 1.27m/s2.
  • #1
Johnny56
1
0

Homework Statement


Data Collected on a Race by a Dragster
Distance (m) - 20.0 when Time (s) 0.945
Distance (m) - 400.0 when Times (s) 8.96
What is the acceleration of the dragster from the 20.0-m mark to the 400.0m mark?
(The answer book says 1.27m/s2 but i don't know how to get it :confused:)

Homework Equations


v=d/t
d= initial velocity*t+1/2at2


The Attempt at a Solution


v=20/0.945
v=21.16 m/s

(2(d-(initial velocity *t)))/t2 = a
(2(380-(21.16*8.02))/8.022 = a
(2*211.10)/64.32 = a
6.56m/s2

i know the reason why I am doing this wrong is because I am using average velocity instead of using the initial velocity but i don't know how to find instantaneous velocity without a graph and i have too little information to draw one
 
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  • #2
You also know that the dragster should have zero velocity at t = 0.
 
  • #3
Using

[tex]d=\frac{Vo+Vf}{2}t[/tex]

you can obtain the Vf, which is the velocity at the 20m mark, and its the initial velocity from the 20m to the 400m.
 
  • #4
you can find the acceleration by finding the initial velocity (should be zero unless otherwise noted) and the final velocity. take and subtract the initial from the final and dived it by the change in time.
 

1. How do you calculate acceleration when given distance and time?

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

2. Can acceleration be negative when given distance and time?

Yes, acceleration can be negative. Negative acceleration, also known as deceleration, occurs when an object is slowing down. This can happen when the initial velocity is greater than the final velocity, resulting in a negative change in velocity.

3. How do you find acceleration without knowing the initial and final velocities?

If the initial and final velocities are unknown, acceleration can still be calculated using the formula a = 2d / t^2, where d is distance and t is time. This formula is derived from the kinematic equations of motion.

4. What units are used for acceleration when given distance and time?

Acceleration is typically measured in meters per second squared (m/s^2) when given distance in meters and time in seconds. However, other units such as feet per second squared (ft/s^2) or kilometers per hour squared (km/h^2) may also be used depending on the context.

5. How does acceleration affect an object's motion when given distance and time?

Acceleration is a measure of how quickly the velocity of an object is changing over time. When an object experiences acceleration, its speed and/or direction of motion is changing. This can result in the object moving faster, slower, or changing direction in a given amount of time.

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