Physics
Motion in One Dimension
Distance and Displacement
11
⚡ Quick Summary
Imagine walking from your house to the store. The total length of the path you take is the distance you traveled. Displacement is simply the straight-line distance and direction from your house to the store, like a shortcut!
No specific formulas given, but understanding the concept of vector addition is important for displacement.
- Distance: The length of the actual path traveled by a particle during a time interval. It's a scalar quantity (only magnitude).
- Displacement: The straight-line distance between the initial and final positions of the particle, with direction from initial to final position. It's a vector quantity (magnitude and direction).
- Displacements add according to the triangle rule of vector addition.
Average Speed
11
⚡ Quick Summary
Think of your average speed on a road trip. It's the total distance you covered divided by the total time the trip took, even if you sped up and slowed down along the way.
v_av = s / (t2 - t1), where s is the distance traveled from time t1 to t2.
- Average Speed: The total distance traveled by a particle divided by the time interval during which the motion occurred. It represents the overall 'rapidity' of the motion.
Instantaneous Speed
11
⚡ Quick Summary
Your instantaneous speed is what your speedometer shows at any exact moment in time. It's how fast you're going *right now*.
v = lim (Δt→0) Δs/Δt = ds/dt, where s is the distance traveled in time t.
- Instantaneous Speed: The speed of a particle at a particular instant in time. It's found by considering the limit of the average speed as the time interval approaches zero.
- Instantaneous speed is also simply referred to as 'speed'.
Average Velocity
11
⚡ Quick Summary
Average velocity is the total displacement divided by the total time taken.
Average velocity = (Total Displacement) / (Total Time)
Average velocity is calculated by dividing the change in position (displacement) by the change in time. It's a vector quantity, meaning it has both magnitude and direction.
Average Acceleration
11
⚡ Quick Summary
Average acceleration is how much the velocity changes over a period of time.
Average acceleration = (Change in Velocity) / (Change in Time)
Average acceleration is the rate of change of velocity. It's calculated by dividing the change in velocity by the change in time. It is also a vector quantity.
Displacement
11
⚡ Quick Summary
Displacement is the shortest distance between the initial and final positions. It's a vector, meaning it has both magnitude and direction.
Δx = x_final - x_initial
Displacement is the change in position of an object. It's different from distance, which is the total length of the path traveled. Displacement can be positive, negative, or zero depending on the direction of motion.
Distance
11
⚡ Quick Summary
Distance is the total length of the path traveled by an object. It's a scalar quantity, so it only has magnitude.
Distance = |Δx1| + |Δx2| + ... where Δxi are the individual displacements along the path.
Distance is always positive or zero. It never decreases as an object moves. It's the total 'odometer' reading of the path traveled.
Speed
11
⚡ Quick Summary
Speed is how fast an object is moving, regardless of direction. It's the distance traveled divided by the time taken.
Average speed = Total distance / Total time
Speed is a scalar quantity. Average speed is the total distance traveled divided by the total time taken. Instantaneous speed is the speed at a particular moment in time.
Velocity
11
⚡ Quick Summary
Velocity is how fast an object is moving in a particular direction. It's the displacement divided by the time taken.
Average velocity = Total displacement / Total time = (x_final - x_initial) / (t_final - t_initial)
Velocity is a vector quantity. Average velocity is the total displacement divided by the total time taken. Instantaneous velocity is the velocity at a particular moment in time. Velocity can be positive or negative, indicating direction.
Acceleration
11
⚡ Quick Summary
Acceleration is how quickly an object's velocity is changing.
Average acceleration = (v_final - v_initial) / (t_final - t_initial)
Acceleration is a vector quantity. It can be positive (speeding up), negative (slowing down or decelerating), or zero (constant velocity). Average acceleration is the change in velocity divided by the time interval. Instantaneous acceleration is the acceleration at a specific moment in time.
Average Velocity
Class 11
⚡ Quick Summary
Average velocity is the total displacement divided by the total time taken. It tells you the 'overall' speed and direction over a period, regardless of how the object moved in between.
Average Velocity = (Total Displacement) / (Total Time)
- Average velocity is a vector quantity.
- It can be positive, negative, or zero depending on the displacement.
- It does not depend on the actual path taken by the object, only on the initial and final positions.
Reaction Time
Class 11
⚡ Quick Summary
Reaction time is the time it takes for you to react to something. For example, the time between seeing a red light and actually hitting the brakes in a car.
Distance travelled during reaction time = (Initial Velocity) * (Reaction Time)
- Reaction time varies from person to person and depends on factors like alertness, distractions, and fatigue.
- During the reaction time, the object continues to move at its initial velocity.
- Stopping distance includes distance travelled during reaction time.
Relationship Between Displacement, Velocity, and Acceleration
11
⚡ Quick Summary
The displacement of an object tells how far it has moved. Velocity tells how fast it's moving and in what direction. Acceleration tells how quickly the velocity is changing. Constant acceleration means the velocity changes steadily.
v = dx/dt, a = dv/dt
- Displacement is the change in position of an object.
- Velocity is the rate of change of displacement with respect to time.
- Acceleration is the rate of change of velocity with respect to time.
- When the acceleration is constant, we can use kinematic equations to relate displacement, velocity, acceleration, and time.