This tutorial explains the concept of acceleration in physics with detailed examples and solutions. Acceleration is a fundamental kinematic quantity that describes how quickly an object's velocity changes over time. Understanding acceleration is crucial for analyzing motion in one and two dimensions.
More problems and their solutions are available on this website.
The average acceleration \(\vec{a}_{avg}\) is a vector quantity (with both magnitude and direction) that describes the rate of change of velocity with respect to time. For an object moving along a straight line, if its velocity changes from \(v_0\) at time \(t_0\) to \(v\) at time \(t\), the average acceleration is given by:
Where:
Note: Acceleration is positive when an object speeds up in the positive direction or slows down in the negative direction. It is negative (deceleration) when an object slows down in the positive direction or speeds up in the negative direction.
What is the acceleration of an object that moves with uniform velocity?
Solution:
If velocity is constant (uniform motion), then \(v = v_0 = V\). Using the acceleration formula:
The acceleration of an object moving at constant velocity is zero because there is no change in velocity over time.
A car accelerates from rest to a speed of 36 km/h in 20 seconds. What is the acceleration of the car in m/s²?
Solution:
Initial velocity: \(v_0 = 0\) (from rest)
Final velocity: \(v = 36 \text{ km/h}\)
First, convert 36 km/h to m/s:
Time interval: \(\Delta t = 20 \text{ s}\)
Average acceleration:
The car accelerates at \(0.5 \text{ m/s}^2\).
A car slows down from a speed of 72 km/h to rest in 25 seconds. What is the acceleration of the car in m/s²?
Solution:
Initial velocity: \(v_0 = 72 \text{ km/h}\)
Final velocity: \(v = 0\) (rest)
Convert 72 km/h to m/s:
Time interval: \(\Delta t = 25 \text{ s}\)
Average acceleration:
The negative sign indicates deceleration (slowing down).
A plane has a takeoff speed of 300 km/h. What is the acceleration in m/s² of the plane if it started from rest and took 45 seconds to take off?
Solution:
Initial velocity: \(v_0 = 0\)
Final velocity: \(v = 300 \text{ km/h}\)
Convert to m/s:
Time interval: \(\Delta t = 45 \text{ s}\)
Average acceleration:
The plane accelerates at approximately \(1.85 \text{ m/s}^2\).
What acceleration is needed to accelerate a car from 36 km/h to 72 km/h in 25 seconds?
Solution:
Initial velocity: \(v_0 = 36 \text{ km/h} = 10 \text{ m/s}\)
Final velocity: \(v = 72 \text{ km/h} = 20 \text{ m/s}\)
Time interval: \(\Delta t = 25 \text{ s}\)
Average acceleration:
The required acceleration is \(0.4 \text{ m/s}^2\).
Starting with a constant velocity of 50 km/h, a car accelerates for 32 seconds at an acceleration of 0.5 m/s². What is the velocity of the car at the end of this period?
Solution:
Initial velocity: \(v_0 = 50 \text{ km/h}\)
Convert to m/s:
Acceleration: \(a = 0.5 \text{ m/s}^2\)
Time interval: \(\Delta t = 32 \text{ s}\)
Using the acceleration formula rearranged to solve for final velocity:
Convert back to km/h:
The final velocity is approximately 107.6 km/h.
How long does it take to accelerate a car from a speed of 50 km/h to a speed of 100 km/h at an acceleration of 1 m/s²?
Solution:
Initial velocity: \(v_0 = 50 \text{ km/h} = 13.89 \text{ m/s}\)
Final velocity: \(v = 100 \text{ km/h} = 27.78 \text{ m/s}\)
Acceleration: \(a = 1 \text{ m/s}^2\)
Using the acceleration formula rearranged to solve for time:
It takes approximately 13.9 seconds.