Rate of Change of Velocity

Discover acceleration - how velocity changes with time, understand uniform and non-uniform acceleration, and learn to calculate acceleration in various scenarios!

Uniform Motion
v = 5 m/s (constant)
Velocity remains constant with time. The change in velocity for any time interval is zero.

Acceleration = 0 m/s²
Non-Uniform Motion
v = 2 → 8 m/s
Velocity varies with time. It has different values at different instants and points.

Acceleration ≠ 0 m/s²
Acceleration Formula
a = (v - u)/t
Where:
a = acceleration (m/s²)
v = final velocity (m/s)
u = initial velocity (m/s)
t = time taken (s)

Acceleration = Change in velocity ÷ Time
Acceleration Calculator
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Select a type of acceleration
Use the buttons below to explore different types of acceleration
Velocity: 0 m/s
Acceleration: +2 m/s²
Direction: Same as motion
Velocity: 10 m/s
Acceleration: -2 m/s²
Direction: Opposite to motion
Velocity vs. Time
Time (s)
Velocity (m/s)
0 1 2 3 4 5
50 40 30 20 10 0
Time: 0 s
Velocity: 0 m/s
Acceleration: +9.8 m/s² (constant)
Velocity vs. Time
Time (s)
Velocity (m/s)
0 1 2 3 4 5
12 9 6 3 0
Time: 0 s
Velocity: 0 m/s
Acceleration: 0 m/s² (varying)
Uniform Acceleration
Time Velocity
Velocity increases steadily
Graph: Straight line with constant slope
Non-Uniform Acceleration
Time Velocity
Velocity changes irregularly
Graph: Curved line with varying slope
Example 7.4
Problem: Starting from rest, Rahul paddles his bicycle to attain a velocity of 6 m/s in 30 s. Then he applies brakes such that the velocity comes down to 4 m/s in the next 5 s. Calculate the acceleration in both cases.
Case 1: Accelerating from rest
Given:
Initial velocity, u = 0 m/s
Final velocity, v = 6 m/s
Time, t = 30 s
Formula:
a = (v - u) / t
Calculation:
a = (6 - 0) / 30 = 6/30 = 0.2 m/s²
Acceleration = +0.2 m/s² (positive)
Case 2: Applying brakes
Given:
Initial velocity, u = 6 m/s
Final velocity, v = 4 m/s
Time, t = 5 s
Formula:
a = (v - u) / t
Calculation:
a = (4 - 6) / 5 = -2/5 = -0.4 m/s²
Acceleration = -0.4 m/s² (negative)

Activity 7.8: Types of Acceleration

Acceleration in Direction of Motion
(a) Positive Acceleration
Example: A car starting from rest and speeding up on a highway. The acceleration helps the car move faster in its direction of motion.
Acceleration Against Direction of Motion
(b) Negative Acceleration (Deceleration)
Example: A moving car applying brakes to stop at a traffic signal. The acceleration opposes the motion, causing the car to slow down.
Uniform Acceleration
(c) Constant Rate of Change
Example: A ball dropped from a height falls with uniform acceleration due to gravity (9.8 m/s²). Its velocity increases by the same amount every second.
Non-Uniform Acceleration
(d) Variable Rate of Change
Example: A car moving through city traffic with frequent stops and starts. The acceleration varies as the driver responds to traffic conditions.

Practice Questions

Q1.
When will you say a body is in (i) uniform acceleration? (ii) non-uniform acceleration?
Answer:
(i) Uniform acceleration: When a body travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time.

(ii) Non-uniform acceleration: When a body's velocity changes at a non-uniform rate, i.e., by unequal amounts in equal intervals of time.
Q2.
A bus decreases its speed from 80 km/h to 60 km/h in 5 s. Find the acceleration of the bus.
Solution:
Given: u = 80 km/h = 80 × (5/18) = 22.22 m/s
v = 60 km/h = 60 × (5/18) = 16.67 m/s
t = 5 s

a = (v - u)/t = (16.67 - 22.22)/5 = -5.55/5 = -1.11 m/s²

Answer: -1.11 m/s² (negative because it's decelerating)
Q3.
A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.
Solution:
Given: u = 0 (starts from rest)
v = 40 km/h = 40 × (5/18) = 11.11 m/s
t = 10 minutes = 600 s

a = (v - u)/t = (11.11 - 0)/600 = 11.11/600 = 0.0185 m/s²

Answer: 0.0185 m/s²
Explore Acceleration
Understanding Acceleration
Acceleration is the rate of change of velocity with time. It measures how quickly an object's velocity changes. When an object moves with changing velocity, it is said to be in accelerated motion.
a = (v - u) / t
SI Unit: metre per second squared (m/s²)
Nature: Vector quantity (has magnitude and direction)
Sign Convention: Positive if in direction of velocity, negative if opposite
Uniform Acceleration
• Velocity changes by equal amounts in equal time intervals
• Acceleration remains constant
• Example: Freely falling body (g = 9.8 m/s²)
• Graph: Straight line
Non-Uniform Acceleration
• Velocity changes by unequal amounts in equal time intervals
• Acceleration varies with time
• Example: Car in city traffic
• Graph: Curved line
Key Points to Remember
• Acceleration can be positive (speeding up) or negative (slowing down)
• Negative acceleration is also called deceleration or retardation
• In uniform motion, acceleration = 0 (velocity is constant)
• Acceleration is a vector quantity - direction matters
• Free fall acceleration on Earth = 9.8 m/s² (downward)
• Units: m/s², km/h², cm/s²