How to Find Acceleration?

To find acceleration, you need to determine the rate of change of an object's velocity over a specific time interval.

Understanding Acceleration

Acceleration (a) is defined as the change in velocity (Δv) divided by the change in time (Δt). This is represented by the equation:

a = Δv/Δt

This equation allows you to measure how quickly velocity changes, with the standard unit being meters per second squared (m/s²). Furthermore, acceleration is a vector quantity, meaning it has both magnitude and direction.

Breaking Down the Components

• Δv (Change in Velocity): This is the difference between the final velocity (v_f) and the initial velocity (v_i) of the object: Δv = v_f - v_i.
• Δt (Change in Time): This is the time interval over which the change in velocity occurs: Δt = t_f - t_i.

Steps to Calculate Acceleration

1. Identify Initial and Final Velocities: Determine the velocity of the object at the beginning (v_i) and end (v_f) of the time interval. Make sure to note the direction as well.
2. Calculate Change in Velocity (Δv): Subtract the initial velocity from the final velocity: Δv = v_f - v_i.
3. Identify Initial and Final Times: Determine the starting time (t_i) and ending time (t_f) of the interval during which the velocity changed.
4. Calculate Change in Time (Δt): Subtract the initial time from the final time: Δt = t_f - t_i.
5. Apply the Formula: Use the formula a = Δv/Δt to calculate the acceleration.
6. Include Units: Report your answer with the correct units (m/s²) and indicate the direction if necessary.

Example

A car accelerates from rest (0 m/s) to 20 m/s in 5 seconds. What is the car's acceleration?

1. Initial Velocity (v_i): 0 m/s
2. Final Velocity (v_f): 20 m/s
3. Initial Time (t_i): 0 s
4. Final Time (t_f): 5 s

• Δv = 20 m/s - 0 m/s = 20 m/s
• Δt = 5 s - 0 s = 5 s

a = Δv/Δt = (20 m/s) / (5 s) = 4 m/s²

The car's acceleration is 4 m/s² in the direction of motion.

Acceleration as a Vector

Because velocity is a vector, acceleration is also a vector. This means direction is important.

• Positive Acceleration: Indicates that the object is speeding up in the positive direction or slowing down in the negative direction.
• Negative Acceleration: Indicates that the object is speeding up in the negative direction or slowing down in the positive direction. Negative acceleration is also referred to as deceleration.

Summary Table

Variable	Description	Units	Formula
a	Acceleration	m/s2	a = Δv/Δt
Δv	Change in Velocity	m/s	Δv = vf - vi
Δt	Change in Time	s	Δt = tf - ti
vf	Final Velocity	m/s
vi	Initial Velocity	m/s
tf	Final Time	s
ti	Initial Time	s